Publications of Yoh Tanimoto

All papers are available either on this page or on arXiv for free.
Besides, papers with the creative commons logo CC-BY are owned by myself (and by coauthors), not by publishers, so that the published final versions are freely available (if I have an electronic copy).

Papers

  1. Inclusions and positive cones of von Neumann algebras,
    J. Operator Theory Vol. 64, Issue 2 (2010), 435-452. published final version in JOT
    arXiv:0801.4259, pdf
    abstract: We consider cones in a Hilbert space associated to two von Neumann algebras and determine when one algebra is included in the other. If a cone is assocated to a von Neumann algebra, the Jordan structure is naturally recovered from it and we can characterize projections of the given von Neumann algebra with the structure in some special situations.
    comment: The contents of this paper is identical with my master thesis. The result and proof are concise and I like them, although the intension was to find new half-sided modular inclusions and no application has been found until now.
  2. Representation theory of the stabilizer subgroup of the point at infinity in Diff(S1),
    Internat. J. Math. Vol. 21, No. 10 (2010), 1297-1335. published final version in IJM
    arXiv:0905.0875, pdf, related presentation in Vietri sul Mare
    abstract: The group Diff(S1) of the orientation preserving diffeomorphisms of the circle S1 plays an important role in conformal field theory. We consider a subgroup B0 of Diff(S1) whose elements stabilize ``the point at infinity''. This subgroup is of interest for the actual physical theory living on the punctured circle, or the real line.
    We investigate the unique central extension K of the Lie algebra of that group. We determine the first and second cohomologies, its ideal structure and the automorphism group. We define a generalization of Verma modules and determine when these representations are irreducible. Its endomorphism semigroup is investigated and some unitary representations of the group which do not extend to Diff(S1) are constructed.
    comment: The first project suggested by Roberto Longo during my PhD study was to classfy the positive energy representations of B0. We expected a situation similar to the Heisenberg group, where there is only one strictly positive energy representation. I found new representations in a few months during the stay in Vienna, which suggested the problem is not simple. After writing up this paper, I started a new project on KMS states and the classification problem still remains open.
  3. Ground state representations of loop algebras,
    Ann. Henri Poincaré Vol. 12, No. 4 (2011), 805-827. published final version in AHP
    arXiv:1005.0270, pdf, related presentation in Göttingen
    abstract: Let g be a simple Lie algebra, Lg be the loop algebra of g. Fixing a point in S1 and identifying the real line with the punctured circle, we consider the subalgebra Sg of Lg of rapidly decreasing elements on R. We classify the translation-invariant 2-cocycles on Sg. We show that the ground state representation of Sg is unique for each cocycle. These ground states correspond precisely to the vacuum representations of Lg.
    comment: I remember that the idea of this paper came to me when I was at Goettingen for a workshop. It didn't take me more than two months.
  4. (with W. Dybalski) Asymptotic completeness in a class of massless relativistic quantum field theories,
    Commun. Math. Phys. Vol. 305, No. 2 (2011), 427-440. published final version in CMP
    arXiv:1006.5430, pdf
    abstract: This paper presents the first examples of massless relativistic quantum field theories which are interacting and asymptotically complete. These two-dimensional models are obtained by an application of a deformation procedure, introduced recently by Grosse and Lechner, to chiral conformal quantum field theories. The resulting models may not be strictly local, but they contain observables localized in spacelike wedges.
    comment: This is the first collaboration with Wojciech Dybalski. My contribution is only the part regarding CFT. Honestly I didn't think that this result was so important at first, but later I found a further generalization of this construction in [8] and the scattering theory extended here was so useful.
  5. (with P. Camassa, R. Longo and M. Weiner) Thermal States in Conformal QFT. I,
    Commun. Math. Phys. Vol. 309, No. 3 (2012), 703-735. published final version in CMP
    arXiv:1101.2865, pdf, related presentations in Göttingen, Bucharest
    abstract: We analyze the set of locally normal KMS states w.r.t. the translation group for a local conformal net A of von Neumann algebras on R. In this first part, we focus on completely rational net A. Our main result here states that, if A is completely rational, there exists exactly one locally normal KMS state φ. Moreover, φ is canonically constructed by a geometric procedure. A crucial role is played by the analysis of the "thermal completion net" associated with a locally normal KMS state. A similar uniqueness result holds for KMS states of two-dimensional local conformal nets w.r.t. the time-translation one-parameter group.
    comment: I heard that this had been a project since Mihály Weiner was previously working in Rome. The main result is so simple, but the actual proof is not that simple as we expected at the beginning. The reviewing process was so quick and they accepted it after one month.
  6. (with W. Dybalski) Infraparticles with superselected direction of motion in two-dimensional conformal field theory,
    Commun. Math. Phys. Vol. 311, No. 2 (2012), 457-490. published final version in CMP CC-BY
    arXiv:1101.5700, pdf
    abstract: Particle aspects of two-dimensional conformal field theories are investigated, using methods from algebraic quantum field theory. The results include asymptotic completeness in terms of (counterparts of) Wigner particles in any vacuum representation and the existence of (counterparts of) infraparticles in any charged representation of a given chiral conformal field theory. Moreover, an interesting interplay between infraparticle's direction of motion and the superselection structure is demonstrated in a large class of examples. This phenomenon resembles electron's momentum superselection expected in quantum electrodynamics.
    comment: This second collaboration with Wojciech has been accomplished almost via email. I had a brief discussion with him during a workshop at Goettingen and all the rest followed online.
  7. Noninteraction of waves in two-dimensional conformal field theory,
    Commun. Math. Phys. Vol. 314, No. 2 (2012), 419-441. published final version in CMP
    arXiv:1107.2662, pdf
    abstract: In higher dimensional quantum field theory, irreducible representations of the Poincaré group are associated with particles. Their counterpart in two-dimensional massless models are "waves" introduced by Buchholz. In this paper we show that waves do not interact in two-dimensional Möbius covariant theories and in- and out-asymptotic fields coincide. We identify the set of the collision states of waves with the subspace generated by the chiral components of the Möbius covariant net from the vacuum. It is also shown that Bisognano-Wichmann property, dilation covariance and asymptotic completeness imply Möbius symmetry.
    Under natural assumptions, we observe that asymptotic fields in Poincaré covariant theory are conditional expectations between appropriate algebras. We show that a two-dimensional massless theory is asymptotically complete and noninteracting if and only if it is a chiral Möbius covariant theory.
    comment: The claimed main result was ready in the previous year, but what I think is really important in this paper is the relations with the modular theory which were found later. Wojciech gave me many suggestions and I reorganized the paper many times. The notations were too complicated.
  8. Construction of wedge-local nets of observables through Longo-Witten endomorphisms,
    Commun. Math. Phys. Vol. 314, No. 2 (2012), 443-469. published final version in CMP CC-BY
    arXiv:1107.2629, pdf, related presentations in Paris, Pavia, Aarhus, Aalborg
    abstract: A convenient framework to treat massless two-dimensional scattering theories has been established by Buchholz. In this framework, we show that the asymptotic algebra and the scattering matrix completely characterize the given theory under asymptotic completeness and standard assumptions.
    Then we obtain several families of interacting wedge-local nets by a purely von Neumann algebraic procedure. One particular case of them coincides with the deformation of chiral CFT by Buchholz-Lechner-Summers. In another case, we manage to determine completely the strictly local elements. Finally, using Longo-Witten endomorphisms on the U(1)-current net and the free fermion net, a large family of wedge-local nets is constructed.
    comment: I consider this as the best result among my single-authored works during my PhD study. I gave a seminar talk on this paper in Italian. I was also invited to ICMP thanks to this paper. An essential part of this work was done just after the earthquake in Japan and the nuclear incident. I remember I was always watching online news and reading documents on the disaster and the people were asking me about it (I was the only Japanse in the math department of Tor Vergata and in the dorm) but I can't remember well how I did this work.
  9. (with P. Camassa, R. Longo and M. Weiner) Thermal States in Conformal QFT. II,
    Commun. Math. Phys. Vol. 315, No. 3 (2012), 771-802. published final version in CMP CC-BY
    arXiv:1109.2064, pdf, related presentations in Göttingen, Bucharest
    abstract: We continue the analysis of the set of locally normal KMS states w.r.t. the translation group for a local conformal net A of von Neumann algebras on the real line. In the first part we have proved the uniqueness of KMS state on every completely rational net. In this second part, we exhibit several (non-rational) conformal nets which admit continuously many primary KMS states. We give a complete classification of the KMS states on the U(1)-current net and on the Virasoro net Vir1 with the central charge c=1, whilst for the Virasoro net Virc with c>1 we exhibit a (possibly incomplete) list of continuously many primary KMS states. To this end, we provide a variation of the Araki-Haag-Kastler-Takesaki theorem within the locally normal system framework: if there is an inclusion of split nets A in B and A is the fixed point of B w.r.t. a compact gauge group, then any locally normal, primary KMS state on A extends to a locally normal, primary state on B, KMS w.r.t. a perturbed translation. Concerning the non-local case, we show that the free Fermi model admits a unique KMS state.
    comment: This is the last one of the papers whose contents are included in my PhD thesis. When the first draft was thought to be ready, I found a gap in the proof of the main theorem in the AHKT paper. I spotted another gap in a slightly different proof of the theorem in the Bratteli-Robinson book. I was almost obsessed with fixing it. Paolo brought a counterexample to these arguments only in a few days after I had reported the gaps, which was beautiful. When the paper got accepted, more than half of the referee report was talking about this gap. I recognized the importance of reading carefully "classical" papers.
  10. (with M. Bischoff) Construction of wedge-local nets of observables through Longo-Witten endomorphisms. II,
    Commun. Math. Phys. Vol. 317, No. 3 (2013), 667-695. published final version in CMP CC-BY
    arXiv:1111.1671, pdf, related presentations in Pavia, Aarhus, Aalborg
    abstract: In the first part, we have constructed several families of interacting wedge-local nets of von Neumann algebras. In particular, there has been discovered a family of models based on the endomorphisms of the U(1)-current algebra of Longo-Witten.
    In this second part, we further investigate endomorphisms and interacting models. The key ingredient is the free massless fermionic net, which contains the U(1)-current net as the fixed point subnet with respect to the U(1) gauge action. Through the restriction to the subnet, we construct a new family of Longo-Witten endomorphisms on the U(1)-current net and accordingly interacting wedge-local nets in two-dimensional spacetime. The U(1)-current net admits the structure of particle numbers and the S-matrices of the models constructed here can be naturally interpreted to represent particle productions.
    comment: The idea came just before the summer vacation in 2011 and we essentially finished it in September. I talked about this paper in the Ph.D. defence although it is not included in the thesis.
  11. (with W. Dybalski) Asymptotic completeness for infraparticles in two-dimensional conformal field theory,
    Lett. Math. Phys. Vol. 103, Issue 11 (2013), 1223-1241. published final version in LMP
    arXiv:1112.4102, pdf
    abstract: We formulate a new concept of asymptotic completeness for two-dimensional massless quantum field theories in the spirit of the theory of particle weights. We show that this concept is more general than the standard particle interpretation based on Buchholz' scattering theory of waves. In particular, it holds in any chiral conformal field theory in an irreducible product representation and in any completely rational conformal field theory. This class contains theories of infraparticles to which the scattering theory of waves does not apply.
    comment: This is the last one of the works done during my Ph.D. The referee process took rather long for LMP (1 year and 4 months). For [12] below it took only 1 month.
  12. (with G. Lechner and J. Schlemmer) On the equivalence of two deformation schemes in quantum field theory,
    Lett. Math. Phys. Vol. 103, Issue 4 (2013), 421-437. published final version in LMP CC-BY
    arXiv:1209.2547, pdf
    abstract: Two recent deformation schemes for quantum field theories on the two-dimensional Minkowski space, making use of deformed field operators and Longo-Witten endomorphisms, respectively, are shown to be equivalent.
    comment: We wanted to construct massive models with particle production, extending [10]. After one year we didn't succeed and decided to publish this part as a letter. The referee process was quick.
  13. Construction of two-dimensional quantum field models through Longo-Witten endomorphisms,
    Forum of Mathematics, Sigma, Vol. 2, e7 (2014). published final version in FMS CC-BY
    arXiv:1301.6090, pdf, related presentations in Aalborg, Rome
    abstract: We present a procedure to construct families of local, massive and interacting Haag-Kastler nets on the two-dimensional spacetime through an operator-algebraic method. An existence proof of local observable is given without relying on modular nuclearity.
    By a similar technique, another family of wedge-local nets is constructed using certain endomorphisms of conformal nets recently studied by Longo and Witten.
    comment: This is so far the best result of mine. Since my Master's study I have wanted to do a construction like this. It is also the first paper in mathematical physics in FoM Sigma.
  14. (with M. Bischoff) Integrable QFT and Longo-Witten endomorphisms,
    Ann. Henri Poincaré, Vol. 16, Issue 2 (2015), 569-608. published final version in AHP, erratum CC-BY
    arXiv:1305.2171, pdf, related presentation in Rome
    abstract: Our previous constructions of Borchers triples are extended to massless scattering with nontrivial left and right components. A massless Borchers triple is constructed from a set of left-left, right-right and left-right scattering functions. We find a correspondence between massless left-right scattering S-matrices and massive block diagonal S-matrices. We point out a simple class of S-matrices with examples.
    We study also the restriction of two-dimensional models to the lightray. Several arguments for constructing strictly local two-dimensional nets are presented and possible scenarios are discussed.
    comment: In 2012, I was working on the Thirring model, Yangians and quantum groups with the hope to find deeper relations to CFT, without success. But thanks to this work I got familiar with integrable models.
  15. Massless Wigner particles in conformal field theory are free,
    Forum of Mathematics, Sigma, Vol. 2, e21 (2014). published final version in FMS CC-BY
    arXiv:1310.4744, pdf, related presentation in Wuppertal
    abstract: We show that in a four dimensional conformal Haag-Kastler net, its massless particle spectrum is generated by a free field subnet. If the massless particle spectrum is scalar, then the free field subnet decouples as a tensor product component.
    comment: I had the idea to combine BGL and Buchholz's scattering theory in 2012 but it was not straightforward because of the regularity condition in the latter. I talked about this in seminars and it turned out that the result of Baumann is not very well-known to our community.
  16. (with D. Cadamuro) Wedge-local fields in integrable models with bound states,
    Commun. Math. Phys., Vol. 340, Issue 2 (2015), 661-697. published final version in CMP CC-BY
    arXiv:1502.01313, pdf, related presentation in Frascati
    abstract: Recently, large families of two-dimensional quantum field theories with factorizing S-matrices have been constructed by the operator-algebraic methods, by first showing the existence of observables localized in wedge-shaped regions. However, these constructions have been limited to the class of S-matrices whose components are analytic in rapidity in the physical strip.
    In this work, we construct candidates for observables in wedges for scalar factorizing S-matrices with poles in the physical strip and show that they weakly commute on a certain domain. We discuss some technical issues concerning further developments, especially the self-adjointness of the candidate operators here and strong commutativity between them.
    comment: This was essentially done in March 2014. Yet, the domain issue is so hard that I had to divide the project into many parts.
  17. Self-adjointness of bound state operators in integrable quantum field theory,
    arXiv:1508.06402, pdf, related presentations in Goslar, Munich
    abstract: We study self-adjoint extensions of operators which are the product of the multiplication operator by an analytic function and the analytic continuation in a strip. We compute the deficiency indices of the product operator for a wide class of analytic functions. For functions of a particular form, we point out the existence of a self-adjoint extension which is unitarily equivalent to the analytic-continuation operation.
    They appear in integrable quantum field theories as the one-particle component of the operators which realize the bound states of elementary particles and the existence of self-adjoint extension is a necessary step for the construction of Haag-Kastler net for such models.
    comment: The project on models with bound states was largely unfinished at the moment of this paper, yet I found these results independently interesting and decided to publish them in this form.
  18. (with D. Cadamuro) Wedge-local fields in integrable models with bound states II. Diagonal S-matrix,
    Ann. Henri Poincaré, Vol. 18, Issue 1 (2017), 233-279. published final version in AHP
    arXiv:1601.07092, pdf
    abstract: We construct candidates for observables in wedge-shaped regions for a class of 1+1-dimensional integrable quantum field theories with bound states whose S-matrix is diagonal, by extending our previous methods for scalar S-matrices. Examples include the Z(N)-Ising models, the AN-affine Toda field theories and some S-matrices with CDD factors.
    We show that these candidate operators which are associated with elementary particles commute weakly on a dense domain. For the models with two species of particles, we can take a larger domain of weak commutativity and give an argument for the Reeh-Schlieder property.
    comment: The Z(3)-Ising model is actually the first model we worked on. For N ≥ 4, some issues remain, but they do not have to do directly with double poles. The paper got unexpectedly long.
  19. Bound state operators and wedge-locality in integrable quantum field theories,
    SIGMA, Vol. 12, 100 (2016), 39 pages. published final version in SIGMA CC-BY-SA
    arXiv:1602.04696, pdf, related presentations in Goslar, Munich
    abstract: We consider scalar two-dimensional quantum field theories with the factorizing S-matrix which has poles in the physical strip. In our previous work, we introduced the bound state operators and constructed candidate operators for observables in wedges.
    Under some additional assumptions on the S-matrix, we show that, in order to obtain their strong commutativity, it is enough to prove the essential self-adjointness of the sum of the left and right bound state operators. This essential self-adjointness is shown up to the two-particle component.
    comment: I haven't yet given up.
  20. (with R. Longo) Rotational KMS states and type I conformal nets,
    Commun. Math. Phys., Vol. 357, Issue 1 (2018), 249-266, published final version in CMP CC-BY
    arXiv:1608.08903, pdf, related presentation in Sendai
    abstract: We consider KMS states on a local conformal net on the unit circle with respect to rotations. We prove that, if the conformal net is of type I, namely if it admits only type I DHR representations, then the extremal KMS states are the Gibbs states in an irreducible representation. Completely rational nets, the U(1)-current net, the Virasoro nets and their finite tensor products are shown to be of type I. In the completely rational case, we also give a direct proof that all factorial KMS states are Gibbs states.
    comment: My first paper towards quantum gravity, hopefully.
  21. (with V. Morinelli and M. Weiner) Conformal covariance and the split property,
    Commun. Math. Phys., Vol. 357, Issue 1 (2018), 379-406. published final version in CMP CC-BY
    arXiv:1609.02196, pdf
    abstract: We show that for a conformal local net of observables on the circle, the split property is automatic. Both full conformal covariance (i.e. diffeomorphism covariance) and the circle-setting play essential roles in this fact, while by previously constructed examples it was already known that even on the circle, Möobius covariance does not imply the split property.
    On the other hand, here we also provide an example of a local conformal net living on the two-dimensional Minkowski space, which - although being diffeomorphism covariant - does not have the split property.
    comment: My main contribution is the 2d counterexample. Misi had been working on the split property for a long time. I remember we discussed an earlier version of his main argument in 2013.
  22. (with D. Cadamuro) Wedge-local observables for factorizing S-matrix with gap in the coupling constant,
    Rev. Math. Phys. Vol. 30, Issue 04 (2018), 1850010, 29 pages. published final version in RMP CC-BY
    arXiv:1612.02073, pdf
    abstract: In the bootstrap approach to integrable quantum field theories in the (1+1)-dimensional Minkowski space, one conjectures the two-particle S-matrix and tries to study local observables. The massless sine-Gordon model is conjectured to be equivalent to the Thirring model, and its breather-breather S-matrix components (where the first breather corresponds to the scalar field of the sine-Gordon model) are closed under fusion. Yet, the residues of the poles in this breather-breather S-matrix have wrong signs and cannot be considered as a separate model.
    We find CDD factors which adjust the signs, so that the breather-breather S-matrix alone satisfies reasonable assumptions. Then we propose candidates for observables in wedge-shaped regions and prove their commutativity in the weak sense.
    comment: We hadn't checked the signs of the residues until 3 months before submission, because the form factor people didn't seem to worry about it. It turned out that a certain range of the coupling constant is easier, which is separated from the Ising model.
  23. (with Y. Otani) Towards entanglement entropy with UV-cutoff in conformal nets,
    Ann. Henri Poincaré Vol. 19, Issue 6 (2018), 1817-1842. published final version in AHP
    arXiv:1701.01186, pdf
    abstract: We consider the entanglement entropy for a spacetime region and its spacelike complement in the framework of algebraic quantum field theory. For a Möobius covariant local net satisfying either a certain nuclearity property or the split property, we consider the von Neumann entropy for type I factors between local algebras and introduce an entropic quantity. Then we implement a cutoff on this quantity with respect to the conformal Hamiltonian and show that it remains finite as the distance of two intervals tends to zero. We compare our definition to others in the literature.
    comment: I was expecting that with nuclearity and UV-cutoff it would be easy to compute entropy. We do have some estimate, but the famous formula c/3 log (l/a) seems far away.
  24. (with R. Longo and Y. Ueda) Free products in AQFT,
    Ann. Inst. Fourier Vol. 69, no. 3 (2019), 1229-1258. published final version in AIF CC-BY
    arXiv:1706.06070, pdf, related presentation in Timisoara
    abstract: We apply the free product construction to various local algebras in algebraic quantum field theory.
    If we take the free product of infinitely many identical half-sided modular inclusions with ergodic canonical endomorphism, we obtain a half-sided modular inclusion with ergodic canonical endomorphism and trivial relative commutant. On the other hand, if we take M\"obius covariant nets with trace class property, we are able to construct an inclusion of free product von Neumann algebras with large relative commutant, by considering either a finite family of identical inclusions or an infinite family of inequivalent inclusions. In two dimensional spacetime, we construct Borchers triples with trivial relative commutant by taking free products of infinitely many, identical Borchers triples. Free products of finitely many Borchers triples are possibly associated with Haag-Kastler net having S-matrix which is nontrivial and non asymptotically complete, yet the nontriviality of double cone algebras remains open.
    comment: We talked about HSMIs in Sendai in 2016 and then Yoshimichi sent us Prop. 3.4. I am hoping that there is a 2d net associated with free product Borchers triples. This is my first joint paper with a Japanese.
  25. (with V. Morinelli) Scale and Möbius covariance in two-dimensional Haag-Kastler net,
    Commun. Math. Phys. Vol. 371, Issue 2 (2019), 619-650. published final version in CMP CC-BY
    arXiv:1807.04707, pdf, related presentation in Firenze
    abstract: Given a two-dimensional Haag-Kastler net which is Poincaré-dilation covariant with additional properties, we prove that it can be extended to a Möbius covariant net. Additional properties are either a certain condition on modular covariance, or a variant of strong additivity. The proof relies neither on the existence of stress-energy tensor nor any assumption on scaling dimensions. We exhibit some examples of Poincaré-dilation covariant net which cannot be extended to a Möbius covariant net, and discuss the obstructions.
    comment: I was expecting that it was easy to extend the 1d result by GLW. Actually it is not and the problem in 4d is widely open. But I like the counterexamples in this paper. The dual net can be a mess.
  26. Ground state representations of some non-rational conformal nets,
    Symmetry Vol. 10, Issue 9 (2018), 415 (Special Issue Mathematical Physics and Symmetry, edited by P. Jorgensen). published final version in Symmetry CC-BY
    arXiv:1807.11723, pdf
    abstract: We construct families of ground state representations of the U(1)-current net and of the Virasoro nets Virc with central charge c >= 1. We show that these representations are not covariant with respect to the original dilations, and those on the U(1)-current net are not solitonic. Furthermore, by going to the dual net of with respect to the ground state representations of Virc, one obtains possibly new family of Möbius covariant nets on S1.
    comment: I have had these results since 2009. Dual nets are very difficult. I expect them to be non conformal. It got published just 5 days after acceptance.
  27. (with S. Carpi, S. Del Vecchio and S. Iovieno) Positive energy representations of Sobolev diffeomorphism groups of the circle,
    Anal. Math. Phys. Vol. 11, Issue 1 (2021) Art. 12. published final version in AMP CC-BY
    arXiv:1808.02384, pdf
    abstract: We show that any positive energy projective representation of Diff(S1) extends to a strongly continuous projective unitary representation of the fractional Sobolev diffeomorphisms Ds(S1) with s>3, and in particular to Ck-diffeomorphisms Diffk(S1) with k >= 4. A similar result holds for the universal covering groups provided that the representation is assumed to be a direct sum of irreducibles. As an application we show that a conformal net of von Neumann algebras on S1 is covariant with respect to Ds(S1), s > 3. Moreover every direct sum of irreducible representations of a conformal net is also Ds(S1)-covariant.
    comment: I thought this were just a part of the following paper on solitons. We tried first Diffk(S1) and found that it worked only for k >= 4. Simone did many important estimates. Sebastiano pointed out that everything could be done for Sobolev groups.
  28. (with S. Del Vecchio and S. Iovieno) Solitons and nonsmooth diffeomorphisms in conformal nets,
    Commun. Math. Phys. Vol. 375, Issue 1 (2020), 391-427. published final version in CMP CC-BY
    arXiv:1811.04501, pdf
    abstract: We show that any solitonic representation of a conformal (diffeomorphism covariant) net on S1 has positive energy and construct an uncountable family of mutually inequivalent solitonic representations of any conformal net, using nonsmooth diffeomorphisms. On the loop group nets, we show that these representations induce representations of the subgroup of loops compactly supported in S1\{-1} which do not extend to the whole loop group.
    In the case of the U(1)-current net, we extend the diffeomorphism covariance to the Sobolev diffeomorphisms Ds(S1), s > 2, and show that the positive-energy vacuum representations of Diff+(S1) with integer central charges extend to Ds(S1). The solitonic representations constructed above for the U(1)-current net and for Virasoro nets with integral central charge are continuously covariant with respect to the stabilizer subgroup of Diff+(S1) of -1 of the circle.
    comment: I feel that I am destined to study things which are non classifiable (in this case solitons, in other cases ground/KMS states, integrable models), or I just tend to construct (counter)examples. In this work I gave some basic ideas, but most estimates and computations were done by Simone and Stefano.
  29. (with S. Carpi and M. Weiner) Unitary representations of the W3-algebra with c >= 2,
    Transform. Groups (2022), published final version in TG CC-BY
    arXiv:1910.08334, pdf
    abstract: We prove unitarity of the vacuum representation of the W3-algebra for all values of the central charge c>=2. We do it by modifying the free field realization of Fateev and Zamolodchikov resulting in a representation which, by a nontrivial argument, can be shown to be unitary on a certain invariant subspace, although it is not unitary on the full space of the two currents needed for the construction. These vacuum representations give rise to simple unitary vertex operator algebras. We also construct explicitly unitary representations for many positive lowest weight values. Taking into account the known form of the Kac determinants, we then completely clarify the question of unitarity of the irreducible lowest weight representations of the W3-algebra in the 2<=c<=98 region.
    comment: The induction part of the proof of unitarity was essentially done during the social dinner in Firenze. I did many computations of VOA for the first time.
  30. (with A. Stottmeister, V. Morinelli and G. Morsella) Operator-algebraic renormalization and wavelets ,
    Phys. Rev. Lett. Vol. 127, 230601 (2021), published final version in PRL
    arXiv:2002.01442, pdf
    abstract: We report on a rigorous operator-algebraic renormalization group scheme and construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets. Causality follows from Lieb-Robinson bounds for harmonic lattice systems. The scheme is related with the multi-scale entanglement renormalization ansatz and augments the semi-continuum limit of quantum systems.
    comment: We wrote this on a suggestion by a physicist. It was not easy to keep the length under the limit.
  31. (with V. Morinelli, G. Morsella and A. Stottmeister) Scaling limits of lattice quantum fields by wavelets,
    Commun. Math. Phys. Vol. 387, 299-360 (2021), published final version in CMP CC-BY
    arXiv:2010.11121, pdf
    abstract: We present a rigorous renormalization group scheme for lattice quantum field theories in terms of operator algebras. The renormalization group is considered as an inductive system of scaling maps between lattice field algebras. We construct scaling maps for scalar lattice fields using Daubechies' wavelets, and show that the inductive limit of free lattice ground states exists and the limit state extends to the familiar massive continuum free field, with the continuum action of spacetime translations. In particular, lattice fields are identified with the continuum field smeared with Daubechies' scaling functions. We compare our scaling maps with other renormalization schemes and their features, such as the momentum shell method or block-spin transformations.
    comment: We bypassed the no-go theorem of Jones, if you wanted. At some point, I was trying to find the Daubechies scaling function without knowing that it was known. The construction is highly nontrivial and it was fortunate that Alex knew it.
  32. (with S. Carpi and M. Weiner) Local energy bounds and strong locality in chiral CFT,
    Commun. Math. Phys. Vol. 390, 169-192 (2022). published final version in CMP
    arXiv:2103.16475, pdf
    abstract: A family of quantum fields is said to be strongly local if it generates a local net of von Neumann algebras. There are very limited methods of showing directly strong locality of a quantum field. Among them, linear energy bounds are the most widely used, yet a chiral conformal field of conformal weight d>2 cannot admit linear energy bounds. We prove that if a chiral conformal field satisfies an energy bound of degree d−1, then it also satisfies a certain local version of the energy bound, and this in turn implies strong locality. A central role in our proof is played by diffeomorphism symmetry. As a concrete application, we show that the vertex operator algebra given by a unitary vacuum representation of the W3-algebra is strongly local. For central charge c>2, this yields a new conformal net. We further prove that these nets do not satisfy strong additivity, and hence are not completely rational.
    comment: Maybe this is the first application of the Driessler-Froehlich theorem where H is not the Hamiltonian?
  33. (with V. Morinelli and B. Wegener) Modular operator for null plane algebras in free fields,
    Commun. Math. Phys. Vol. 395, 331-363 (2022). published final version in CMP CC-BY
    arXiv:2107.00039, pdf
    abstract: We consider the algebras generated by observables in quantum field theory localized in regions in the null plane. For a scalar free field theory, we show that the one-particle structure can be decomposed into a continuous direct integral of lightlike fibres, and the modular operator decomposes accordingly. This implies that a certain form of QNEC is valid in free fields involving the causal completions of half-spaces on the null plane (null cuts). We also compute the relative entropy of null cut algebras with respect to the vacuum and some coherent states.
    comment: I essentially had the decomposition already 2019. Benedikt and Vincenzo did much about ANEC and QNEC.
  34. (with C. Raymond and J. E. Tener) Unitary vertex algebras and Wightman conformal field theories,
    Commun. Math. Phys. Vol. 395, 299-330 (2022), published final version in CMP CC-BY
    arXiv:2203.10795, pdf
    abstract: We prove an equivalence between the following notions: (i) unitary Möbius vertex algebras, and (ii) Wightman conformal field theories on the circle (with finite-dimensional conformal weight spaces) satisfying an additional condition that we call uniformly bounded order. Reading this equivalence in one direction, we obtain new analytic and operator-theoretic information about vertex operators. In the other direction we characterize OPEs of Wightman fields and show they satisfy the axioms of a vertex algebra. As an application we establish new results linking unitary vertex operator algebras with conformal nets.
    comment: I didn't expect that the axioms of vertex algebras could imply analytical conditions like uniformly bounded order (brought to me by James and Chris in February 2021). Since then, this work was done entirely online.
  35. (with M.S. Adamo and L. Giorgetti) Wightman fields for two-dimensional conformal field theories with pointed representation category,
    Commun. Math. Phys. Vol. 404, 1231-1273 (2023), published final version in CMP CC-BY
    arXiv:2301.12310, pdf
    abstract: Two-dimensional full conformal field theories have been studied in various mathematical frameworks, from algebraic, operator-algebraic to categorical. In this work, we focus our attention on theories with chiral components having pointed braided tensor representation subcategories, namely where there are automorphisms whose equivalence classes form an abelian group. For such theories, we exhibit the explicit Hilbert space structure and construct primary fields as Wightman fields for the two-dimensional full theory. Given a finite collection of chiral components with automorphism categories with vanishing total braiding, we also construct a local extension of their tensor product as a chiral component. We clarify the relations with the Longo-Rehren construction, and illustrate these results with concrete examples including the U(1)-current.
    comment: I was wondering why we had the combination of the same sectors in this ([21]), while Longo-Rehren combines the conjugate sectors. It turns out that in the U(1)-current the map from -α to α is brading-preserving.
  36. (with C. Jäkel) Towards integrable perturbation of 2d CFT on de Sitter space,
    Lett. Math. Phys. Vol. 113, article 89 (2023), published final version in LMP CC-BY
    arXiv:2301.12468, pdf
    abstract: We describe a procedure to deform the dynamics of a two-dimensional conformal net to possibly obtain a Haag-Kastler net on the de Sitter spacetime. The new dynamics is given by adding a primary field smeared on the time-zero circle to the Lorentz generators of the conformal net. As an example, we take an extension of the chiral U(1)-current net by a charged field with conformal dimension d < 1/4. We show that the perturbing operators are defined on a dense domain.
    comment: Since when I saw this, I had been thinking how to perturb CFT. I think this paper gives a partial answer (to be completed).
  37. (with W. Dybalski and A. Stottmeister) Lattice Green functions for pedestrians: Exponential decay,
    Rev. Math. Phys. Vol. 36, Issue No. 06, Article 2430005 (2024). published final version in RMP CC-BY
    arXiv:2303.10754, pdf
    abstract: The exponential decay of lattice Green functions is one of the main technical ingredients of the Bałaban's approach to renormalization. We give here a self-contained proof, whose various ingredients were scattered in the literature. The main sources of exponential decay are the Combes-Thomas method and the analyticity of the Fourier transforms. They are combined using a renormalization group equation and the method of images.
    comment: After around 15 years of my career, I wanted to construct models in higher dimension. Hopefully this is a start.
  38. (with W. Dybalski and A. Stottmeister) The Bałaban variational problem in the non-linear sigma model,
    arXiv:2403.09800, pdf
    abstract: The minimization of the action of a QFT with a constraint dictated by the block averaging procedure is an important part of Bałaban's approach to renormalization. It is particularly interesting for QFTs with non-trivial target spaces, such as gauge theories or non-linear sigma models on a lattice. We analyze this step for the O(4) non-linear sigma model in two dimensions and demonstrate, in this case, how various ingredients of Bałaban's approach play together. First, using variational calculus on Lie groups, the equation for the critical point is derived. Then, this non-linear equation is solved by the Banach contraction mapping theorem. This step requires detailed control of lattice Green functions and their integral kernels via random walk expansions.
    comment: The non-linear sigma models should be just renormalizable. Here the Banach fixed point theorem is used but I wonder why that works. Maybe it is related with the fact that the extremal point is the minimum.
  39. (with M.S. Adamo and Y. Moriwaki) Osterwalder-Schrader axioms for unitary full vertex operator algebras,
    arXiv:2407.18222, pdf
    abstract: Full Vertex Operator Algebras (full VOA) are extensions of two commuting Vertex Operator Algebras, introduced to formulate compact two-dimensional conformal field theory. We define unitarity, polynomial energy bounds and polynomial spectral density for full VOA. Under these conditions and local C1-cofiniteness of the simple full VOA, we show that the correlation functions of quasi-primary fields define tempered distributions and satisfy a conformal version of the Osterwalder-Schrader axioms, including the linear growth condition.
    As an example, we show that a family of full extensions of the Heisenberg VOA satisfies all these assumptions.
    comment: I think I finally understood the Euclidean formulation of 2d CFT. When I was in Tokyo with Maria Stella, we met Yuto at Komaba and the collaboration started immediately.

Proceedings

  1. Construction of wedge-local QFT through Longo-Witten endomorphisms,
    Proceedings of the XVII International Congress on Mathematical Physics, World Scientific (2013). published final version CC-BY
    arXiv:1209.1370, pdf, slides
    (I do not have an electronic copy, however, I own the copyright of the paper and the contents are the same as the arXiv version/the pdf file below)
    abstract: We review our recent construction of operator-algebraic quantum field models with weak localization property. Chiral components of two-dimensional conformal fields and certain endomorphisms of their observable algebras play a crucial role. In one case, this construction leads to a family of strictly local (Haag-Kastler) nets.
    comment: Only 3 or 4 weeks before the conference I got the idea of constructing massive nets. In Aalborg there were significantly less particiants (358 according to the official website) than other places (e.g. 618 in Prague, 623 in Rio de Janeiro, over 500 in Lisbon). The choice of place considerably matters, or maybe it was because of the financial crisis.
  2. Operator-algebraic construction of integrable QFT,
    Oberwolfach Reports, Vol. 12, Issue 2 (2015). 867-869. published final version CC-BY
    pdf
    (I have not been asked to sign any copyright transfer format)
    comment: Written for mathematicians (operator-algebraists) with the emphasis on half-sided modular inclusions and Borchers triples.
  3. Towards construction of integrable QFT with bound states,
    Proceedings of the 14th Marcel Grossmann meeting, World Scientific (2017). published final version CC-BY
    pdf, slides

    comment: The conference was huge, yet in our pararell session there were usual people. I myself tried rather to listen to other sessions.
  4. Towards Haag-Kastler nets for integrable QFT with bound states (in Japanese),
    RIMS Kokyuroku No. 2010. published final version CC-BY
    pdf, slides
    (I have not been asked to sign any copyright transfer format)
    comment: The title of the workshop is "mathematics of QFT" or something like it, but not many people talked about it.
  5. KMS states on conformal QFT,
    to appear in the proceedings of the MSJ-SI Sendai. CC-BY
    pdf, slides
    (I have not been asked to sign any copyright transfer format)
    comment: We thought that no type II representation appears in any KMS state, but I found an error in the proof after the talk. The slides here have been corrected.
  6. Half-sided modular inclusions (and free products in AQFT),
    to appear in Oberwolfach Reports CC-BY
    pdf
    (I have not been asked to sign any copyright transfer format)
    comment: This is presented in the workshop "Reflection positivity" and many of the AQFT people didn't talk about RP at all.
  7. Free products and AQFT,
    to appear in the proceedings of OT27. CC-BY
    pdf
    (I have not been asked to sign any copyright transfer format)
    comment: There was an interesting session on quantum information. I learned for the first time about Conne's embedding conjecture.
  8. Strong locality beyond linear energy bounds,
    to appear in Oberwolfach Reports. CC-BY
    pdf
    (I have not been asked to sign any copyright transfer format)
    comment: I got sick at Oberwolfach, for the second time.

Ph.D. Thesis

Low dimensional quantum field theory and operator algebras, pdf, October 2011. Supervisor: Roberto Longo
comment: This thesis won the "Premio Michele Cuozzo", which recognizes the best Ph.D. thesis in mathematics at Italian universities during the academic year 2011-2012 among applicants, awarded at Giornata di Dipartimento 2012, Rome. Here is a text extracted from a press-release (in Italian) about the prize by Tor Vergata university.

Articles for general public

  1. (with S. Kurokawa) A study on radiation dose estimation with no scientific integrity: a critical analysis of the Miyazaki-Hayano paper 2 (in Japanese),
    "Kagaku (science)" magazine, April 2019 issue, Iwanami Shoten, Publishers.
    pdf, summary, related articles
  2. (with S. Kurokawa) Supplements to the critical analysis of the Miyazaki-Hayano papers, 1 (in Japanese),
    "Kagaku (science)" magazine, June 2019 issue, Iwanami Shoten, Publishers.
    pdf
  3. (with S. Kurokawa) Supplements to the critical analysis of the Miyazaki-Hayano papers, 2 (in Japanese),
    "Kagaku (science)" magazine, July 2019 issue, Iwanami Shoten, Publishers.
    pdf
  4. (with S. Kurokawa) Comments on the investigation reports by Fukushima Medical University and the University of Tokyo on allegations regarding papers on radiation dose estimates in Date City,
    "Kagaku (science)" magazine, August 2019 electronic issue, Iwanami Shoten, Publishers.
    pdf
    abstract: There are serious concerns with the investigations carried out by Fukushima Medical University and the University of Tokyo on allegations regarding two papers by Makoto Miyazaki and Ryugo Hayano (i.e. Miyazaki-Hayano Papers 1 and 2)[1,2]. These investigations fail to address several important issues raised in the allegations. In particular, some discrepancies among the main Figures in Paper 2 [2] remain unexplained, and the claimed absence of underestimation of lifetime doses is illogical.
  5. (with M. Oshikawa, Y. Hamaoka, K. Kageura, S. Kurokawa and J. Makino) Comments on "Individual external dose monitoring of all citizens of Date City by passive dosimeter 5 to 51 months after the Fukushima NPP accident (series): 1." ,
    arXiv:2001.11912, pdf
    abstract: We point out numerous inconsistencies and inappropriate statements in M. Miyazaki and H. Hayano, Journal of Radiological Protection 37, 1 (2016).
  6. (with S. Kurokawa, M. Oshikawa, Y. Hamaoka, K. Kageura and J. Makino) Further comments on "Individual external dose monitoring of all citizens of Date City by passive dosimeter 5 to 51 months after the Fukushima NPP accident (series): 1." : Inconsistencies in Table 1 2014 Q3 and Figure 4f ,
    arXiv:2003.05403, pdf
    abstract: We point out serious inconsistencies of the first paper of the series, written by Makoto Miyazaki and Ryugo Hayano, which discusses the correlation between the personal doses of the citizens of Date City measured by glass badges with the ambient dose rates measured by six airborne surveys. The last of the six airborne survey was made in the period of 2014 Q3 (from October 2014 to December 2014). The real number of participants of the period is about 14,500; however, in Table 1 2014 Q3 it is written that the number of participants is 21,080 and in Fig. 4f 21,052. We conclude that the analysis of the paper with respect to Table 1 2014 Q3 and Fig. 4f are done without using real correct data and we cannot obtain any meaningful information from the table and figure. Since the period 2014 Q3 is also included in Fig. 5 of the second paper of the series, it is quite possible that Fig. 5 of the second paper is made on the basis of, at least partially, false data and is not reliable.
  7. (with Y. Hamaoka, K. Kageura, S. Kurokawa, J. Makino and M. Oshikawa) Comments on "Individual external dose monitoring of all citizens of Date City by passive dosimeter 5 to 51 months after the Fukushima NPP accident (series): II. Prediction of lifetime additional effective dose and evaluating the effect of decontamination on individual dose." ,
    arXiv:1812.11453 (the second part of this submission), pdf
    abstract: We we point out inconsistencies, obvious mistakes and inappropriate state-ments in [1], which were not discussed in the earlier Letter [2] by one of us (SK).
  8. (with Y. Hamaoka, K. Kageura, S. Kurokawa, J. Makino, and M. Oshikawa) Comments on "Publisher’s Note" on papers on individual external dose monitoring of all citizens of Date City,
    MetaArXiv:n6fyh, pdf
    abstract: We point out that the recently published Publisher’s Note concerning two retractions in Journal of Radiological Protection and the retraction notices contain various incorrect statements, misrepresentations of facts and omission of important events.
    comment: This letter has been rejected by JRP without review, because they "consider that the matter is now closed". The reader can see our manuscript and determine whether the matter is closed or not.
  9. (with K. Kageura, Y. Hamaoka, S. Kurokawa, J. Makino, and M. Oshikawa) On “Commentary: The responsibility of the Japanese media, the Fukushima accident and the use of personal data”by T. Sawano et al.,
    QJM: An International Journal of Medicine, Volume 114, Issue 12, December 2021, Pages 901–902. published final version in QJM
    MetaArXiv:exy6p, pdf
    abstract: This Commentary, which alleges the media misportrayal of two papers (now retracted), 1,2 not only takes a position that disregards the Declaration of Helsinki, which emphasizes the rights and interests of individual research subjects, but also contains the following errors and misleading statements.
  10. (with Y. Hamaoka, K. Kageura, S. Kurokawa, J. Makino, and M. Oshikawa) The mishandling of scientifically flawed articles about radiation exposure, retracted for ethical reasons, impedes understanding of the scientific issues pointed out by Letters to the Editor,
    The Journal of Scientific Practice and Integrity , Published online October 23, 2022. published final version in JoSPI
    MetaArXiv:wrmep, pdf, pdf in Japanese,
    abstract: We discuss the editorial handling of two papers that were published in and then retracted from the Journal of Radiological Protection (JRP). The papers, which dealt with radiation exposure in Date City, were retracted because "ethically inappropriate data were used". Before retraction, four Letters to the Editor pointing out scientific issues in the papers had been submitted to JRP. The Letters were all accepted or provisionally accepted through peer review. Nevertheless, JRP later refused to publish them. We examine the handling by JRP of the Letters, and show that it left the reader unapprised of a) the extent of the issues in the papers, which went far beyond the use of unconsented data, and b) the problems in the way the journal handled the matter. By its actions in this case, JRP has enabled unscientific, unfounded and erroneous claims to remain unacknowledged. We propose some countermeasures to prevent such inappropriate actions by academic journals in future.
    abstract: I learned a lot from writing this paper about how some journals and institutions do not help investigations of cases of suspected scientific misconduct, how well they are documented and the present case is (unfortunately) not isolated.
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