The fishnet CFT is a non-unitary CFT of two matrix complex scalar fields interacting via a single quartic potential. The chiral nature of the interaction strongly constrains the Feynman diagrams arising at each order in perturbation theory, those that survive are of fishnet type. In this talk, I will present the TBA equations for the conformal dimensions of multi-magnon local operators in this theory. I will emphasize the need to diagonalize suitable graph-building operators in order to determine the asymptotic data, dispersion relation and S matrix, on which the TBA relies. A dual version of the TBA equations, relating D-dimensional graphs to two-dimensional sigma models, will also be examined. The last part of the talk will be devoted to the presentation of the underlying non-compact spin chain and of additional results regarding diagonalization of graph-building operators. --------------------- Part of London Integrability Journal Club. New participants please register at integrability-london.weebly.com for the link.

I will give an overview of recent progress in understanding string theory in AdS3 backgrounds with a mixture of Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz three-form flux. Such theories are integrable, but provide many features not encountered in the more familiar case of pure Ramond-Ramond flux. In this talk I will explore the analytic structure of the dispersion relation of the world-sheet excitations and how it relates to the crossing equations of the two-particle S matrix. Determining the dressing phases of the mixed flux S matrix is the next major step in using integrability to the AdS3/CFT2 correspondence. -------- Part of London Integrability Journal Club. New participants please register at integrability-london.weebly.com to receive the link.

The first half of the talk will be a review of the main ingredients of bulk reconstruction: the Ryu-Takayanagi formula and subregion duality, the JLMS theorem, error correction and the complexity conjecture. The second half will be about my recent and current work on "modular Berry phases"--a type of Berry phase which characterizes the entanglement structure of a quantum state. We will see that the bulk curvature in AdS is (up to an integral transform) a special case of the modular Berry phase, though the concept has many other applications which we may or may not discuss.

Recently there have been renewed interest and relevant progress in calculating overlaps between periodic multiparticle states and integrable boundary states. They appear in quite distinct parts of theoretical physics including statistical physics and the gauge/string duality. I will give a summary of known overlap formulas and analyze the connection between selection rules and symmetries. I will introduce a nesting procedure for boundary states which provides the factorizing overlaps for higher rank algebras automatically. This method can be used for the calculation of the asymptotic all-loop 1-point functions in AdS/dCFT. In doing so I will present the solutions of the YBE for the K-matrices with centrally extended su(2|2) symmetry and the generic overlaps of the corresponding boundary states. Based on 2004.11329 ------------------------- Part of London Integrability Journal Club. Please register at integrability-london.weebly.com/ for the zoom link

Integrability techniques have played a major role in the study the AdS/CFT correspondence, providing an accurate description of different string theoretic observables beyond the weak or strong coupling perturbation theory. However, the case of string on certain AdS_3 backgrounds provided new challenges in the form of massless excitations. Difficulties in incorporating these into the integrable description have led to disagreements concerning the energy of massive physical states. In general integrable theories, massless and massive sectors can generally be treated separately. We know this cannot be the case in AdS_3, but a full TBA description of the interaction between the sectors is yet to be found. Surprisingly, such a description can found in a family of integrable field theories — homogeneous sine-Gordon models. Here, one can take a double scaling limit of the adjustable parameters and zoom into a regime described by a TBA where the massless sector does not decouple and contributes to the energy of massive particles at the same order as for which the Bethe ansatz would suffice in a massive theory. ------- Part of London Integrability Journal Club. Please register at integrability-london.weebly.com for the link.

In his paper in 1979, Polyakov envisaged a possibility of reformulating the gauge theory as a Principal Chiral Model defined on a space of loops and discussed "the loop-space integrability". This idea, together with a closely related idea of the loop equation, led to numerous important results in matrix models and 2d gauge theories, but its application to four-dimensional gauge theories had only limited success. Now, after 50 years, we have a concrete example of integrable four-dimensional gauge theory, N=4 SYM. However integrability in N=4 SYM is formulated mostly in terms of local operators, although important progress has been made in constructing the Yangian for the Wilson loops. In this talk, I will present a framework which would bridge these two distant notions of integrabililty. The key player in the story is a correlation function of a local operator and the Wilson loop. I reformulate the gauge-theory computation of this observable as an overlap between an energy eigenstate of a spin chain and a matrix product state (MPS). Unlike standard MPS's discussed in the literature, our MPS has infinite bond dimensions in order to accommodate infinite dimensionality of the space of loops. It provides an "intertwiner" between integrable structures of the local operators and the Wilson loops, and in particular implies the existence of a special set of deformations of the Wilson loop which satisfy the QQ-relation. I will also explain how to formulate a nonperturbative bootstrap program based on the results obtained in this framework and compute the correlator of the circular BPS Wilson loop and general non-BPS operators at finite coupling, emphasizing the relation to and the difference from other observables that were computed by a similar approach. ----------------- Part of London Integrability Journal Club. Please register using the form at integrability-london.weebly.com

We review a proof of bijection between eigenstates of the Bethe algebra and solutions of Bethe equations written as a Wronskian quantisation condition or as QQ-relations on Young diagrams. Furthermore, it is demonstrated that the Bethe algebra is maximal commutative and it has simple spectrum every time it is diagonalisable. The proof covers rational gl(m|n) spin chains in the defining representation with the famous Heisenberg spin chain being a particular subcase. The proof is rigorous (no general position arguments are used). We do not rely on the string hypothesis and moreover we conjecture a precise meaning of Bethe strings as a consequence of the proposed proof. A short introduction with necessary facts about polynomial rings will be given at the beginning of the talk. Based on 2004.02865 NOTE: Part of London Integrability Journal Club. Please register at integrability-london.weebly.com to participate.

There are indications that "traditional" GR physics at the horizon and usual assumptions of locality cannot provide a consistent description of black holes. The fuzzball paradigm suggests that "traditional" GR physics at the horizon should be relaxed and that string theory provides the right degrees of freedom to have a non-trivial structure at the scale of the horizon. I'll review how this idea has emerged from the analysis of the Strominger-Vafa black hole and its implication for the AdS3/CFT2 duality. For link to the meeting, please email damian.galante@kcl.ac.uk.

Computing scalar products is a non-trivial problem in the context of the Algebraic Bethe Ansatz. In this talk I comment about the different problems one encounter and how to easily compute recurrence relations for scalar products, even beyond SU(2). I will also present a possible explanation for the existence of determinant representations of the scalar products. NOTE: Part of London Integrability Journal Club. Please register at integrability-london.weebly.com

I will give a summary of recent progress in the computation of exact results in the presence of superconformal defects, focusing on a special class of defect correlators. Along the way, I will comment on the possibility of using integrability and propose various future directions. NOTE: to receive the link please fill the registration form at integrability-london.weebly.com

I will give an informal review of some of the recent developments on reproducing the page curve in semi-classical gravity. I will then compare and contrast these results to older results from the study of holographic 2d CFT with sparse spectra and large central charge. In these quantum systems, there is a natural understanding of the CFT duals of the bulk semiclassical classical saddles that are responsible for evading information loss. I will end with some cautionary remarks explaining why I believe it is too early to declare the information problem "solved". For Zoom link please contact damian.galante at kcl.ac.uk

I will give an introduction to the Quantum Spectral Curve in AdS/CFT. This is an integrability-based framework which provides the exact spectrum of planar N = 4 super Yang-Mills theory (and of the dual string model) in terms of a solution of a Riemann-Hilbert problem for a finite set of functions. I review the underlying QQ-relations starting from simple spin chain examples, and describe the special features arising for AdS/CFT. I will also present some pedagogical examples to show the framework in action. Lastly I will briefly discuss its recent applications for correlation functions. Based on the review arXiv:1911.13065. NOTE: online seminar using Zoom. Please register to the mailing list on integrability-london.weebly.com to participate.

It is often suggested that integrable 2d sigma models should be renormalizable, however this relationship has only previously been checked in the 1-loop approximation. The aim of this work is to understand what happens beyond 1-loop. We shall pedagogically introduce the lambda- and eta-models, and non-abelian duality. Based on these examples, we confirm that classically integrable sigma models appear to be 2-loop renormalizable if supplemented with a particular choice of finite counterterms, i.e. quantum corrections to the target space geometry. The 2-loop beta-function of the lambda-model is computed, matching the known results for groups and symmetric spaces in the limit when the lambda-model becomes the corresponding non-abelian dual model. This leads to the statement that non-abelian duality commutes with the RG flow beyond 1-loop order. NOTE: Please register to the mailing list at integrability-london.weebly.com to receive the link for the Zoom meeting.

I will present some results on the 1d Super-Conformal Field Theory (SCFT) living on a 1/2-BPS line defect in a 4d N=4 SCFT. The main realization of this setup being Wilson lines in N=4 Super-Yang-Mills (SYM). After reviewing what the modern numerical bootstrap have to say about this problem I will describe how analytic bootstrap methods can efficiently produce the perturbative expansion at strong coupling in the planar theory. NOTE: This will be an online seminar using Zoom. Please register at integrability-london.weebly.com to receive the link

"I will review recent advancements in the development of the Separation of Variables (SoV) program for rational higher rank spin chains, motivated by the recent appearance of SoV-type structures in AdS/CFT. I will discuss the main approaches for constructing a separated variable basis which include diagonalising the B-operator and the action of fused transfer matricies on a suitable vacuum state. I will explain how these approaches are linked and demonstrate how they can be unified into a single framework governed by Yangian representation theory. The outcome is that for any finite-dimensional su(n) spin chain the wave functions (Bethe vectors) factorise into an ascending product of Slater determinants in Baxter Q-functions, allowing us to immediately link this operatorial construction of states with the recently developed functional approach of computing scalar products and form factors." NOTE: this will be an online seminar using Zoom. To participate please fill the registration form on integrability-london.weebly.com.

The notion of integrability can be extended to systems with boundaries. In large volume and finite temperature, the free energy of such systems – unlike those periodic – contains a non-extensive piece, called g-function, with many physical interpretations. We present a method [1906.07733] hybrid of [1003.5542, 1007.1148, 1809.05705] to calculate the g-function from the TBA partition function. NOTE: Thus is an online seminar using Zoom. Please follow the registration link on https://integrability-london.weebly.com/

----------------- Part of London Integrability Journal Club. If you are a new participant, please register using the form at integrability-london.weebly.com.

t.b.a. ------- Part of the London Integrability Journal Club. If you are not already registered, please sign up at integrability-london.weebly.com/registration.html. The link will be emailed.

All day event: speakers include Andrea Fontanella (Surrey), Ana Loureiro (Kent), Marika Taylor (Southampton) and Takato Yoshimura (King's College). Details: https://www.kent.ac.uk/smsas/personal/tcd/webpages/MP/semps7.htm

http://personal.maths.surrey.ac.uk/st/M.Wolf/conferences/smuk2013/index.html