Part of London Integrability Journal Club. New participants should register using the form at integrability-london.weebly.com. The link will be emailed.

The first recorded lecture of the London Theory Institute for PhD Students. Link to recording and problems (to be solved in live Zoom session next Monday) as well as registration details at https://lonti.weebly.com/ and https://youtu.be/CGDNipeuVEs Instantons, or solutions to the self dual Yang Mills (SDYM) equations are well known solutions, introduced in the mid 70s and played a role in a host of applications in QFT and String Theory. This talk will show a simple brane construction which allows the computation of the moduli space of solutions to the SDYM equations, introduce the student to the world of quivers, and demonstrate simple computations which allow evaluations of these moduli spaces.

In this talk we will consider the spectrum of anomalous dimensions in N=4 super-Yang-Mills and related theories. We will first discuss the emergence of quantum chaos as one goes from infinite to finite N and how the perturbative spectrum is described by GOE random matrix theory. We will then describe how the integrability of the planar-limit can be used to rewrite the computation of the leading 1/N corrections to the one-loop anomalous dimensions in terms of scalar products of off-shell Bethe states or, alternatively, hexagon-like functions.---- Part of London Integrability Journal Club. If you are a new participant, please register filling the form at integrability-london.weebly.com. The link will be emailed.

Part of the London Black Hole Information Paradox Journal Club (for Zoom link, please subscribe here: https://forms.gle/wLYi4A72tEUwuzGK6)

Two-dimensional field theories deformed by Zamolodchikov's TTbar operator have recently attracted the attention of theoretical physicists due to the many important links with string theory and AdS/CFT. In this talk, I will describe various classical and quantum aspects of this particular irrelevant perturbation, including its geometrical interpretation at the classical level. I will also introduce a generalisation of this geometrical framework to 4D field theories, and discuss some of the interesting differences with the 2D case. ---- Part of London Integrability Journal Club. If you are a new participant, please register filling the form at integrability-london.weebly.com. The link will be emailed.

One incarnation of the AdS/CFT correspondence is the duality between the symmetric product orbifold of T4 and superstrings on AdS3xS3xT4 with one unit of NS-NS flux. Compared to other instances of AdS/CFT, this duality is much simpler and can in principle be fully understood. I will give a broad overview of the inner workings of the duality from a worldsheet CFT point of view, physical lessons and connections to integrability. ---- Part of London Integrability Journal Club. If you are a new participant, please register filling the form at integrability-london.weebly.com. The link will be emailed.

I will review the QQ-system and oscillator construction of Q-operators for su(r+1) spin chains and discuss its generalisation to so(2r) spin chains. ----- Part of London Integrability Journal Club. If you are a new participant, please register filling the form at integrability-london.weebly.com. The link will be emailed.

In this talk I give an overview of the Yangian symmetry of Feynman integrals. After reviewing the connection between AdS/CFT integrability and the Yangian symmetry of massless Feynman graphs, I discuss the idea to bootstrap Feynman integrals based on the Yangian constraints. Then I show that also in the massive case large classes of Feynman integrals are constrained by a Yangian extension of dual conformal symmetry. When translated to momentum space, this leads to a novel massive generalization of ordinary conformal symmetry. Finally, I argue that these features of massive Feynman integrals can be understood as the integrability of planar scattering amplitudes in a massive version of the so-called fishnet theory, which is obtained as a double-scaling limit of N=4 super Yang-Mills theory on the Coulomb branch. ---- Part of London Integrability Journal Club. If you are a new participant, please register filling the form at integrability-london.weebly.com. The link will be emailed.

t.b.a. ------- Part of London Integrability Journal Club. If you are a new particiant, please register using the form on our website integrability-london.weebly.com. The link will be emailed.

An important example among the 2d geometrical critical phenomena is the critical Q-state Potts model, which describes the percolation in the limit Q-->1. In this talk I will consider the problem of determining the geometrical four-point functions (cluster connectivities) in this model. Connections with the minimal models are made which uncover remarkable properties of the Potts amplitudes. Such properties allow to deduce the existence of "interchiral conformal blocks" which can be constructed using the degeneracy in the Potts spectrum. Using these, I will then determine the four-point functions through numerical bootstrap. In addition, I will also discuss the logarithmic nature of the Potts CFT and hints of a full analytic solution of the model. ----- Part of London Integrability Journal Club. New participants please register using the form at integrability-london.weebly.com. The link will be emailed.

I will describe the role of 't Hooft operators in 4d Chern-Simons theory and applications to integrability. --------------------- Part of London Integrability Journal Club. If you are a new participant, please register using the form at integrability-london.weebly.com. The link will be emailed.

There is a class of representations of quantum groups, referred to as prefundamental representations, that plays an important role in the solution of integrable models. The first example of such representations was given by V. Bazhanov, S. Lukyanov and A. Zamolodchikov in the context of two dimensional conformal field theory in order to construct Baxter Q-operators as transfer matrices. At the same time, there is a rather exceptional quantum group that governs the integrable structure of the one dimensional Hubbard model and plays a fundamental role in the AdS/CFT correspondence. In this talk I will introduce prefundamental representations for this quantum group, explain their basic properties and discuss some of their applications. ------------- Part of London Integrability Journal Club. New participants please register at integrability-london.weebly.com to receive the link. (Registration is needed only once).

Twenty years ago Maldacena, Ooguri and Son constructed a modular invariant partition function for the Euclidean black hole (cigar) NLSM. They also proposed an expression for the corresponding density matrix. This result played a key role in the formulation of the remarkable conjecture by Ikhlef, Jacobsen and Saleur that the Euclidean black hole NLSM underlies the critical behaviour of a certain integrable spin chain. In this talk we critically reexamine the above proposals. The talk is based on the recent (unpublished) joint work with V. Bazhanov and G. Kotousov. ------------------------ Part of London Integrability Journal Club. New participants please register at integrability-london.weebly.com to receive the link. (Registration is needed only once).

The D0-brane matrix model (the BFSS matrix model and the BMN matrix model) can describe various objects including type IIA black zero-brane, M-theory black hole, M2-branes and M5-branes. We study this theory from several different angles. We put the emphasis on the importance of the dynamics of eigenvalues of matrices, and more generally, color degrees of freedom. Furthermore we explain how the Euclidean theory can be studied by using the Monte Carlo method, and discuss the future directions. If you have a good idea we can test it on computer together! Part of the Black Hole Information Paradox Journal Club. Please email damian.galante@kcl.ac.uk for link to the meeting.

The Yang-Baxter equation is an important equation that appears in many different areas of physics. It signals the presence of integrable structures which appear in topics ranging from condensed matter physics to holography. In this talk I will discuss a new method to find all regular solutions of the Yang-Baxter equation by using the so-called boost automorphism. The main idea behind this method is to use the Hamiltonian rather than the R-matrix as a starting point. I will demonstrate our method by classifying all solutions of the Yang-Baxter equation of eight-vertex type. I will also consider certain 9x9 and 16x16 solutions and give new integrable models in all of these cases. As a further application, I will discuss all integrable deformations of R-matrices that appear in the lower-dimensional cases of the AdS/CFT correspondence. -------------------------- Part of London Integrability Journal Club. New participants please register at integrability-london.weebly.com for the link. (Registration is only needed once).

In this talk I will discuss new properties of the complex SYK model in comparison with the Majorana one. I’ll mostly focus on spectrum of operators and the effective low energy action of the complex SYK model. In this case the conserved U(1) charge contributes a compact scalar field to the effective action in addition to the Schwarzian term. Part of the Black Hole Information Paradox Journal Club. Please email damian.galante@kcl.ac.uk for link to the meeting.

The g-function is a measure of degrees of freedom associated to a boundary of two-dimensional quantum field theories. In integrable theories, it can be computed exactly in a form of the Fredholm determinant, but it is often hard to evaluate numerically. In this paper, we derive functional equations---or equivalently integral equations of the thermodynamic Bethe ansatz (TBA) type---which directly compute the g-function in the simplest integrable theory; the sinh-Gordon theory at the self-dual point. The derivation is based on the classic result by Tracy and Widom on the relation between Fredholm determinants and TBA, which was used also in the context of topological string. As a side result, we present multiple integrals of Q-functions which we conjecture to describe a universal part of the g-function, and discuss its implication to integrable spin chains. ------------------------- Part of London Integrability Journal Club. New participants please register at integrability-london.weebly.com to receive the link.

Most recent discussions of holography in AdS_2/CFT_1 have focused on the Schwarzian and JT gravity. However, the AdS dual of SYK is expected to, in addition, contain an infinite tower of massive fields. The interactions for these fields are in principle fixed by the SYK correlation functions. We review the construction of all-point correlation functions in SYK. We comment on the difficulties in finding a coherent description of the bulk tower of fields. Part of the Black Hole Information Paradox Journal Club. Please email damian.galante@kcl.ac.uk for link to the meeting.

I review the emergence of JT gravity from the SYK model, and the calculation of correlation functions in JT gravity. I motivate the need for a new observable distinct from entanglement entropy to fully decode emergent gravity, and propose as such an observable a quantum generalization of the entropy of multiple measurements on a dynamical system. Part of the Black Hole Information Paradox Journal Club. Please email damian.galante@kcl.ac.uk for link to the meeting.

The goal is to have a general discussion about replica wormholes and the black hole information problem. To start things off, we will discuss the question of whether an ensemble interpretation is necessary for the replica wormhole computations of the entropy. Part of the Black Hole Information Paradox Journal Club. Please email damian.galante@kcl.ac.uk for link to the meeting. NOTE THAT THE TIME/DATE OF THE TALK HAS BEEN CHANGED.