Papers I recently read/was interested in (not (only) on AQFT)

The list here shows the recent interest of Tanimoto, mainly outside AQFT. They are not exhaustive and it is not meant that I have understood them or read them thoroughly. Rather, they might be a starting point of new research in AQFT. Furthermore, my comments may contain (even substantial) misunderstandings.
I keep this page public in order to share what I am/was thinking about.
Note: the date indicates when I started reading the paper and not the date of publication.

(8. 2024) King, The U(1) Higgs model. II. The infinite volume limit

Here the infinite volume limit is taken and some interesting ideas for rotation invariance are presented, but it is not really proven. The problem is that the convergence of the infinite volume limit depends on correlation inequalities, which are incompatible when rotated.
(7. 2024) Kong, Runkel, Algebraic Structures in Euclidean and Minkowskian Two-Dimensional Conformal Field Theory

After doing this, I got curious about CFT on Riemann surfaces. It turned out that they are rather defined by compatibility with each other, so having a model on the Riemann sphere is not at all enough to construct the "same model" on other surfaces. Why this should be possible for non CFT is unclear to me, if a functional integration measure is not available.
(6. 2024) Gies, Ziebell, Asymptotically Safe QED

I just wondered what is known about nonperturbative QED (apart from the expectation that it is "trivial"), searched for asymptotic safety in QED. This is one of (very) few papers.
(5. 2024) Guillarmou, Gunaratnam, Vargas, 2d Sinh-Gordon model on the infinite cylinder

It seems that this is the Euclidean probabilistic version of the construction I proposed here. I would like to check the OS axioms.
(4. 2024) Gawędzki, Lectures on conformal field theory

I came across this and understood that the vertex operators in the free field are considered as compactified Gaussian free field. It is still not clear to me whether they satisfy the Glimm-Jaffe axioms.
(3. 2024) Lüscher, Mack, Global conformal invariance in quantum field theory

As Fröhlich-Osterwalder-Seiler does not treat the case of conformal group, I read this. Interestingly, the Wightman functions are not extended to the cylinder (it's unclear how to extend them to points which are not in a single copy of the Minkowski space).
(2. 2024) Avigad, Massot, Mathematics in Lean

I had done a tutorial in Lean 3, but that was not enough to start writing new proofs. This book explains the structures, hierarchies in very concrete examples.
(1. 2024) Fröhlich, Osterwalder, Seiler, On virtual representations of symmetric spaces and their analytic continuation

I expected that the paper applied to the conformal group. It turns out it does not.
(12. 2023) Tsukada, String Path Integral Realization of Vertex Operator Algebras

Measures on the space of distributions on S¹ are introduced and reproduce the Hilbert spaces of lattice VOAs, but not of the Euclidean theory as I expected.
(11. 2023) Schlingemann, Euclidean field theory on a sphere

I wanted a version of the OS axioms for sphere (cf. Barata-Jäkel-Mund). The arguments depend essentially on virtual representations, but it's unclear how this extends to distributions (Schwinger/Wightman).
(10. 2023) Dimock, Hurd, Construction of the two-dimensional sine-Gordon model for β < 8π

They prove the convergence of partition functions as N tends to infinity. However, here the UV regularization is given by the momentum cutoff and not lattice regularization. As a consequence, they can compare the "activities" with different N directly. It's not clear how to do this on lattices.
(9. 2023) Davydov, Bogomolov multiplier, double class-preserving automorphisms and modular invariants for orbifolds

It seems to claim that there are some chiral components of 2d CFT which can be extended to two different full CFT with the same decomposition into sectors with respect to chiral components.
(8. 2023) Giuliani, Mastropietro, Rychkov, Gentle introduction to rigorous Renormalization Group: a worked fermionic example

This gives a rigorous approach to the renormalization group method, taking a fermionic model. They consider the space of all interactions, extract relevant parts, give an appropriate norm and use the fixed point theorem. It is nice that all these are carried out without too many complications as in the bosonic case.
(7. 2023) Bałaban, (Higgs)_2,3 Quantum fields in a finite volume I

The first paper by Bałaban on his methods of small and large field split. Many technical details are postponed to further papers.
(6. 2023) Kravchuk, Qiao, Rychkov, Distributions in CFT II. Minkowski Space

The paper is about the implication from axioms on the OPE in CFT, but it contains a nice review of regularity conditions in the Osterwalder-Schrader reconstruction.
(5. 2023) Felder, Fröhlich, Keller, On the structure of unitary conformal field theory. I. Existence of conformal blocks

One of few works which treat CFT explicitly as a Euclidean field theory. I want to make sure that the algebraic setting such as (full) VOA, with appropriate regularity, gives OS axioms.
(4. 2023) Dimock, Yuan, Structural stability of the RG flow in the Gross-Neveu model

When I was studying this, the paper appeared on arXiv and I got interested because there is no large-small field split (the Gross-Neveu model is written in terms of Grassmannian), and it is just renormalizable. Apart from that, I enjoyed the paper very much because many vague concepts in renormalization are carried out explicitly in this model.
(3. 2023) Feldman, Knörrer, Trubowitz, Fermionic Functional Integrals and the Renormalization Group

This paper requires some basics on Grassmann integrals and Gaussian, so I needed to study them.
(2. 2023) Avigad, Lewis, van Doorn, Logic and Proof

This is a documentation on formal proofs in Lean, with some basics on logic and formal languages. I read this as I got interested in writing in Lean again. I tried to do the tutorials again and it went more smoothly than I had expected.
(1. 2023) Ceyhan, Faulkner, Recovering the QNEC from the ANEC

I knew this paper but took another look when I was visiting Gandalf Lechner in Erlangen. Lemma 2 works easily if the state is given by an unitary action of the algebra and another of the commutant. We tried to find a way to approximate a general state with such states.
(12. 2022) King, The U(1) Higgs model. I. The continuum limit

This paper constructs the U(1)-Higgs model (correlation functions) using the Bałaban-Dimock methods. The effective action is different from that of Dimock (given by a certain degree of perturbation theory).
(11. 2022) Dimock, The Renormalization Group According to Balaban - III. Convergence

The third part of three on Bałaban's methods. The ultraviolet stability is shown. I wonder whether the partition function actually converges, and how to prove it.
(10. 2022) Schottenloher, A Mathematical Introduction to Conformal Field Theory

I have known this book for a long time, but noticed only recently that it contained the Osterwalder-Scharder axioms for CFT. It's unclear whether the unitarity in the VOA sense implies reflection positivity, but locality in VOA seems similar to the Euclidean locality.
(9. 2022) Creutzig, Kanade, McRae, Gluing vertex algebras

I think we have a corresponding notion of brading reverseing and extension of conformal nets on circle.
(8. 2022) Schellekens, Conformal field theory

I was searching for the proof of uniqueness of 3-point functions. It wasn't so immediate to translate physicists' claim to a proof for Wightman fields.
(7. 2022) Moriwaki, Full vertex algebra and bootstrap -- consistency of four point functions in 2d CFT

This gives a formulation of (full) 2d CFT. Apparently the convergence of the formal series expansion of 4p functions is assumed.
(6. 2022) Loebbert, Lectures on Yangian Symmetry

This lecture explains how factorizing S-matrices arise from Yangian symmetry.
(5. 2022) Huang, Kong, Full field algebras

This paper should tell how two chiral components should be combined to a full (two-dimensional) CFT. I wonder whether unitarity is preserved under this procedure.
(4. 2022) Bałaban, O'Carroll, Low Temperature Properties for Correlation Functions in Classical N-Vector Spin Models

This outlines the way to obtain correlation functions using Bałaban's methods. The details need to be worked out in examples.
(3. 2022) Dimock, The Renormalization Group According to Balaban - II. Large fields

The second part of three on Bałaban's methods. The notations are complicated but the ideas are similar to those in part I. This is about the large field.
(2. 2022) Carlip, Quantum Gravity: a Progress Report

Somehow I wanted to know the current (20 years ago) status of quantum gravity. This covers from the canonical/covariant quantization to loop quantum gravity and string theory.
(1. 2022) Reshetikhin, Smirnov, Hidden Quantum Group Symmetry and Integrable Perturbations of Conformal Field Theories

This is about the SU_q(2)-action on the sine-Gordon model. Apparently the action is not unitary and I am not sure whether this can have a meaningful interpretation in AQFT.
(12. 2021) Bernard, Maassarani, Mathieu, Logarithmic Yangians in WZW models

Yangian should act on the WZW models. I wonder what this means in terms of local algebras.
(11. 2021) Lechner, Scotford, Deformations of half-sided modular inclusions and non-local chiral field theories

They find that the lightlike intersection of the massive free field deformed in the sense of Buchholz-Lechner-Summers is trivial. It is nice that this is settled after 13 years.
(10. 2021) Reshetikhin, Smirnov, Hidden Quantum Group Symmetry and Integrable Perturbations of Conformal Field Theories

The sine-Gordon model is claimed to be the deformation of the massless free boson with some primary field.
(9. 2021) Dybalski, Mund, Interacting massless infraparticles in 1+1 dimensions

This paper shows that some extensions of the U(1)-current CFT are "interacting". I think the scattering ampulitudes have much to do with braiding.
(8. 2021) Dimock, The Renormalization Group According to Balaban - I. Small fields

The first part of three on Bałaban's methods. It took me a long time to be accustomed with the framework. I started to read it seriously since I watched this seminar by Jaffe.
(7. 2021) Jubb, On Causal State Updates in Quantum Field Theory

This appears to show how far the framework of Fewster-Verch can go. The restriction that the coupled system is also a local QFT is very important.
(6. 2021) Brukner, A no-go theorem for observer-independent facts

A very clear account of why we should be careful with two or more observers in quantum mechanics. I wonder how "observer-dependent facts" can be formulated.
(5. 2021) Bałaban, Imbrie, Jaffe, Exact Renormalization Group for Gauge Theories

A review by Bałaban himself of his series of papers on Yang-Mills theory.
(4. 2021) Rosen, Renormalization of the Hilbert Space in the Mass Shift Model

Some explicit formulae are given for the quadratic "interaction". On the de Sitter space, this should be realized on the same Hilbert space.
(3. 2021) Moriwaki, Two-dimensional conformal field theory, current-current deformation and mass formula

The claim seems to be that, by perturbing the SU(2)-WZW model by the product of currents, one should obtain a family of conformal field theories with c = 1. I think it's not difficult to have the latter in the Haag-Kastler setting.
(2. 2021) Glimm, Jaffe, Quantum physics

I remembered that the proofs of various correlation inequalities are written in this book, which are often omitted in reviews.
(1. 2021) Glimm, Jaffe, Remark on the Existence of φ⁴₄

When one wants to construct only the correlation functions, this paper gives the recipe of how to choose the coupling constant (so that the two-point functions converge, and hope the rest is nontrivial). I finally understood this in this paper.
(12. 2020) Powers and Størmer, Free States of the Canonical Anticommutation Relations

I read the proof of the Hilbert-Schmidt condition for the CAR for the first time. I wanted to see the unitary but seems difficult.
(11. 2020) Hollowood, 6 Lectures on QFT, RG and SUSY

What is believed by physicists is compactly explained.
(10. 2020) Neumaier, Renormalization without infinities

It is argued that renormalization is a reparametrization. Type B models in this article are quite interesting. They are formal Hamiltonians that make sense only after certain limit where the bare coupling tends to zero.
(9. 2020) Skinner, Advanced Quantum Field Theory, Chapter 1-3

Although the treatment of QFT is the conventional one, I liked these notes because they explain how the action changes as the scale changes, telling honestly that it includes nonlocal terms in principle.
(8. 2020) Skinner, The Renormalization Group

I learned the renormalization flow and relevant/irrerevant operators. I wonder whether I will ever be able to make sense of them.
(7. 2020) Tuite, Zuevsky, A Generalized Vertex Operator Algebra for Heisenberg Intertwiners

A formula for charged intertwiner for the Heisenberg algebra can be found. I tried to check that some of them are primary.
(6. 2020) Cardy, Mussardo, Form factors of descendent operators in perturbed conformal field theories

This paper suggests that there is a pair of Virasoro algebras acting on the space of the massive Ising model. I do not know how this can be consistend with this, where the even part of the Ising model is shown to be a single Virasoro module with c=1/2.
(5. 2020) Glimm, Jaffe, Quantum physics

Classic. It was good to have a fresh look at timeless achievements during the lockdown.
(4. 2020) Epstein, Moschella, de Sitter symmetry of Neveu-Schwarz spinors

I wanted to see an explicit construction of the massive free fermion on the de Sitter spacetime. I couldn't find it and studied this instead.
(3. 2020) Fernández, Fröhlich, Sokal, Random-Walks, Critical Phenomena, and Triviality in Quantum Field Theory

I was looking for a single complete example of QFT constructed through lattice. This book contains a general theory.
(2. 2020) Hill, Learning Scientific Programming with Python

With the COVID-19 emergency in Italy, I just tried some of the basic epidemiological models. The author makes nice examples available online here.
(1. 2020) Daubechies, Ten Lectures on Wavelets

A book by the discoverer of the Daubechies wavelets. The proofs are detailed and quite readable. I happened to use wavelets in my work.
(12. 2019) Atanasov, 2D CFT and the Ising Model

Apparently the massive 2d Ising model contains the disorder parameter, so it should not be the perturbation by the field with dimension 1/2.
(11. 2019) Procházka, Rapčák, W-algebra Modules, Free Fields, and Gukov-Witten Defects

I decided to read this because I wrote a paper on the W₃-algebra and it says that W-algebras appear in a gauge theory. It turns out that there are a huge family of Y-algebras.
(10. 2019) Zamolodchikov, Integrals of motion in scaling 3-state Potts model field theory

I just noticed that there is the W₃-algebra (but with c=4/5) is related with an integrable model.
(9. 2019) Kay, Remarks on matter-gravity entanglement, entropy, information loss and events

I had been wondering why no one talks about the entanglement between matter (quantum fields) and gravity. In fact, Kay does.
(8. 2019) Kac, Vertex Algebras for Beginners

I finally studied a bit vertex algebras.
(7. 2019) Bouwknegt, McCarthy, Pilch, The W₃ algebra

The definition in this book of the W₃ algebra appears wrong. As the commutator between W fields contains an infinite sum, it does not make sense to talk about universal enveloping algebra naively. Consequently, Verma modules cannot be constructed by quotienting the universal enveloping algebra.
(6. 2019) Fateev, Zamolodchikov, Conformal quantum field theory models in two dimensions having Z₃ symmetry

It is hard to imagine how they came up with this free field realization.
(5. 2019) Osborne, Continuum Limits of Quantum Lattice Systems

I want to see whether the usual massive free state can be constructed in this way.
(4. 2019) Afkhami-Jeddi, Colville, Hartman, Maloney, Perlmutter, Constraints on Higher Spin CFT₂

A factorization of the Kac deterinant of the W_N-algebras is discussed.
(3. 2019) Mizoguchi, Determinant formula and unitarity for the W₃ algebra

Apparently we have a proof of unitarity for a continuous spectum of modules.
(2. 2019) Bernard, LeClair, Quantum group symmetries and nonlocal currents in 2D QFT

These nonlocal currents must have something to do with wedge-local fields.
(1. 2019) Zamolodchikov, Integrable Field Theory from Conformal Field Theory

If these field are realized as operators in two-dimensional CFT, I think there is a chance that "integrable pertubation" could make sense, à la constructive CFT.
(12. 2018) Babujian, Foerster, Karowski, Exact form factors in integrable quantum field theories: the scaling Z(N)-Ising model

Finally I understand something about double poles in factorizing S-matrix. If I trust their axioms, then apparently the polarization-free generator cannot preserve the particle number because some singular term arises from their computations in Appendix.
(11. 2018) Castro-Alvaredo, Bootstrap Methods in 1+1-Dimensional Quantum Field Theories: the Homogeneous Sine-Gordon Models

When I was searching for the UV limit of the sine-Gordon model, I happened to find that the SU(3)_2 homogeneous sine-Gordon model has been constructed by myself. The CFT in the UV limit has been also constructed, so we should be able to understand the integrable perturbation in this case.
(10. 2018) Reshetikhin, Smirnov, Hidden quantum group symmetry and integrable perturbations of conformal field theories

I met Cornelius Schmidt-Colinet in Cardiff and he informed me of this paper which contains a concise review of integrable perturbation. The case of the restricted sine-Gordon model appears to be the most studied one.
(9. 2018) Casini, Huerta, A c-theorem for the entanglement entropy

Gerardo told me that there are two types of renormalization groups, with and without cutoff. I found it also here, and I just realized that Casini and Huerta wrote it explicity.
(8. 2018) Simmons-Duffin, TASI Lectures on the Conformal Bootstrap

I met the author in Banff and we discussed whether Wightman axioms are guaranteed by conformal bootstrap. Henning Rehren pointed out that locality was not very clear. Later Ryo Suzuki informed me of this paper, so locality gives additional constraints.
(7. 2018) Inci, Kappeler, Topalov, On the regularity of the composition of diffeomorphisms

This is a very useful article on group properties of Sobolev spaces. In one weekend I read the relevant parts for this paper.
(6. 2018) Hossenfelder, Lost in math

I think the title of this book should have been "Lost in beauty" or something like it. I believe that one of the problems of high-energy physics is that they do not use proper math, or even any consistent framework.
(5. 2018) Chollet, Deep Learning with Python

This is an extremely practical book, explains from what commands you type in to install packages to concrete source codes with concrete data with the addresses from which one can download them. Interestingly, the author suggests that reasoning is currently out of reach for deep learning models. I wonder extracting formal statements from math papers requires reasoning or it is close to mechanical translation.
(4. 2018) Sun, Schur-Weyl duality for quantum groups

I tried (and failed) to construct QFT with quantum group statistics. It turned out that Hecke algebra H_q(n) does not act nicely on the n-particle space.
(3. 2018) Witten, Notes on Some Entanglement Properties of Quantum Field Theory

I tried to understand path integral (with not much successs). I really do not understand which conjectures/calculations are more plausible and which are not, because their arguments are based on an assumption which they say they know is false, yet they use anyway. .
(2. 2018) Roos, Inner-outer factorization of analytic matrix-valued functions

I came up with a new type of analytic intertwiner between certain represetations of the symmetric group and wondered whether this can be applied to integrable QFT.
(1. 2018) Kaye, The Mathematics of Logic

I wanted to understand the difference between first- and higher-order logics, and why many automated theorem provers use first-order logic.
(12. 2017) Coleman, Thun, On the prosaic origin of the double poles in the sine-Gordon S-matrix

I had read this before when I was trying to construct wedge observables. But it only "explains" double poles and did not help. I read this again because a referee of my paper asked to a similar stuff in our paper. It just does not make sense because it "explains" poles in terms of Lagrangian, which we do not have.
(11. 2017) Loos, Irving, Szegedy, Kaliszyk, Deep network guided proof search

I am just curious about the current status of automatic theorem proving. Probably one of the differences between board games like go and math is that there is a fixed goal in a game while we move the target in math.
(10. 2017) Brydges, Fröhlich, Seiler, On the construction of quantized gauge fields. I.

I wanted to see how the continuum limit works in examples, and this appears to be a nice example. I am hoping to translate it to the Haag-Kastler setting.
(09. 2017) Nakayama, Scale invariance vs conformal invariance

I suspect that if one assumes that the vacuum is separating for the (future) light cone and its modular group is the dilations, then conformal covariance should follow.
(08. 2017) Palmer, Tracy, Two-dimensional Ising correlations: Convergence of the scaling limit

This appears to have completed a proof of the Osterwalder-Schrader axioms for the continuum limit of the 2d Ising model. From here, it took almost 30 years to prove conformal covariance (by S.Smirnov).
(07. 2017) Catterall, Kaplan, Unsal, Exact lattice supersymmetry

I was searching for some topics concerning lattice continuum limit which can be dealt with in AQFT. Supersymmetry, probably?
(06. 2017) Bousso, Casini, Fisher, Maldacena, Entropy on a null surface for interacting quantum field theories and the Bousso bound

They claim that the algebras of null planes are trivial by some arguments on scaling dimensions. I wonder whether/how this can be compatible with my models.
(06. 2017) Hollowood, 6 Lectures on QFT, RG and SUSY

I think I've for the first time understood what superrenormalizability and UV-finiteness mean.
(05. 2017) Wall, A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices

Related with Casini-Teste-Torroba below, the author uses the existence of observables on the nul plane. Section 5 seems almost to argue against it.
(04. 2017) Casini, Teste, Torroba, Modular Hamiltonians on the null plane and a Markov property of the vacuum state

They conjecture the modular operator for some regions with lightlike boundary. I think this can be done for free fields. I wonder whether they hold for interacting theories.
(03. 2017) Unruh, Wald, Information Loss

The authors say that it's ok that a pure state evolves into a mixed state because after the evaporation of a black hole there is no Cauchy surface. It sounds reasonable to me (in other papers in physics, the terms "pure" and "mixed" are used in an abusive way and often make no sense).
(02. 2017) Rattazzi, Rychkov, Tonni, Vichi, Bounding scalar operator dimensions in 4D CFT

The seminal paper of the recent trend of higher-dimensional conformal bootstrap. I wondered whether there was any possibility to exploit the unitarity in a different way so I took a look.
(02. 2017) Serone, Spada, Villadoro, The Power of Perturbation Theory

The results are interesting but seem to depend on the existence of a Borel-summable model.
(10. 2015?) Casini, Huerta, Remarks on the entanglement entropy for disconnected regions

Physicist often talk about "reduced density matrix" for local algebras and call it the "modular Hamiltonian", which simply does not exist. It is similar to "eigenvalues" of self-adjoint operators on an infinite-dimensional Hilbert space (instead of spectrum). I am almost hoping that there are situations where the difference matter.
(04. 2015?) Almheiri, Marolf, Polchinski, Sully, Black Holes: Complementarity or Firewalls?

I don't understand why the subsystems of radiations in question commute each other (which is necessary to talk about entanglement between them). I consulted several physicists and they didn't know either. Anyway I started to think about entropy in AQFT after having read this paper.
(12. 2013) Barata, Jäkel, Mund, The ${\mathscr P}(\varphi)_2$ Model on the de Sitter Space

They claim to have constructed many two-dimensional (possibly interacting) models from operator-algebraic construction on the de Sitter spacetime. When I listened to a talk by Jäkel, I thought that there could be four-dimensional/conformal variations, so I started to study it. Among related papers are Guido-Longo, Borchers-Buchholz.
(10. 2013) Kovacs, N=4 supersymmetric Yang-Mills theory and the AdS/SCFT correspondence

Another thesis on N=4 SYM with detailed expalanations on the perturbative calculation.
(10. 2013) Mandelstam, Light-cone superspace and the ultraviolet finiteness of the N=4 model

A perturbative proof that the beta-function vanishes in N=4 SYM. Actually it is claimed that each perturbative contribution is finite in a certain gauge.
(10. 2013) Genovese, Conformal Invariance in Quantum Field Theory

A thesis on conformal invariance. I wanted to find a thesis which explains the basics like this.
(9. 2013) Rivasseau, From Perturbative to Constructive Renormalization

A book on the works of Rivasseau and others.
(7. 2013) 't Hooft, Planar diagram field theories

A lecture note given by 't Hooft. More comprehensible than the original papers.
(7. 2013) Rivasseau, Construction and Borel summability of planar 4-dimensional Euclidean field theory

This tries to sum up rather directly planar Feynman diagrams. I haven't understood why only Borel summability is expected here, while 't Hooft succeeded to prove the convergence of Green functions (see below).
(7. 2013) 't Hooft, Rigorous construction of planar diagram field theories in four-dimensional Euclidean space

This proves that planar perturbative series is convergent in massive theories. Apparently it is open in massless theories, in particular in SYM. I wonder whether reflection positivity is formally preserved.
(6. 2013) Serban, Integrability and the AdS/CFT correspondence

Another (and importantly, shorter) review on the integrability of N=4 SYM.
(6. 2013) Austing, Wheater, Convergent Yang-Mills Matrix Theories

Matrix Yang-Mills theory (without spacetime dependence) is considered. Although it is completely different from the continuous theory, one can see that the perturbative series behaves better when N of SU(N) is large.
(6. 2013) Gomez, Gunnesson, Hernandez, The Ising model and planar N=4 Yang-Mills

Some papers claim that the perturbative series in N=4 SYM is convergent (also P.8 of this) but I've never seen one proof. This paper claims that the radius of convergence is related to phase transition of the Ising model.
(5. 2013) Aharony, Gubser, Maldacena, Ooguri, Oz, Large N Field Theories, String Theory and Gravity

Presumably the most famous review on the topic.
(5. 2013) Seiberg, Witten, The D1/D5 System And Singular CFT

Apparently they study the CFT part of AdS₃/CFT₂ correspondence.
(5. 2013) Ahn, Bombardelli, Exact S-matrices for AdS₃/CFT₂

Full S-matrices are proposed in RR AdS₃/CFT₂ correspondence through integrability technique.
(4. 2013) Maldacena, Ooguri, Strings in AdS_3 and the SL(2,R) WZW Model. Part 1: The Spectrum

This paper conjectures the Hilbert space of the string theory in AdS₃ as a representation space of the SL(2,R)-loop group.
(4. 2013) Weinberg, Minimal fields of canonical dimensionality are free

It is shown that massless particles (generated by fields) in conformal field theories are free. "Particle" here means an irreducible representation of the spacetime symmetry, if I understood correctly. I want to see what it implies to N=4 SYM (see below), which is conformal. Maybe it does not contain any massless spectrum?
(4. 2013) Beisert et al., Review of AdS/CFT Integrability

It has been claimed that N=4 super Yang-Mills theory in the planar limit is integrable and equivalent to the classical string theory on AdS spacetime. Integrability, if it is true, would be interesting to me because it would make a rigorous construction possible. However, the main argument in this review seems to be that there are certain integrable structures in the perturbative coefficients.
(3. 2013) Quella, Formfactors and locality in integrable models of quantum field theory in 1+1 dimensions

This paper proves the local commutativity theorem for integrable S-matrix with poles. I wonder what would be an operator-algebraic correspondent.
(3. 2013) Schreiber, AQFT from n-functorial QFT

This paper tries to make connection between topological/functorial QFT and algebraic QFT. The results look still preliminary because the properties of the vacuum are not considered.

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