In this talk, I will discuss how to compute the spectral curve of "segmented strings" in AdS_3. The motion of a string in this target space is integrable and the worldsheet theory can be discretized while preserving integrability. The corresponding embeddings are segmented strings, which generalize piecewise linear strings in flat space. I will present several examples. Next, I will introduce "brane tilings", which are doubly-periodic planar bipartite graphs. I will show that the motion of a closed segmented string can be embedded into the mutation dynamics of a certain brane tiling. This will enable us to compute the spectral curve by taking the determinant of the dressed adjacency matrix of the tiling. ----------- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.

The application of random matrix techniques in QCD and non-Abelian gauge theories in general has a long history e.g. in counting Feynman diagrams, going back to 't Hooft and others. In this talk I will focus on a different aspect that relates the two in the low energy spectrum of the QCD Dirac operator, as initiated by Shuryak and Verbaarschot. First, I will explain what is the approximation studied here where spectral statistics of random matrices apply, and where for example the technique of orthogonal polynomials can be useful in comparing to QCD lattice data. It is given by a particular finite volume low energy limit, the epsilon regime of chiral perturbation theory of Gasser and Leutwyler. I will mention how QCD parameters like quark masses, zero-modes, finite lattice spacing or chemical potential can be incorporated into the random matrix ensemble. In the last part I will discuss some recent work with my former student Tim Wurfel on the inclusion of finite temperature, that leads out of the standard classes of random matrices, but still remains analytically tractable. This talk is mainly based on the review arXiv:1603.06011 and the paper with Tim arXiv:2110.03617; part of the London TQFT Journal Club; it will be possible to follow this talk online (please register at https://london-tqft.vercel.app)

In this talk, I will present a procedure to extract the generalised eigenvectors of a non-diagonalisable matrix by considering a diagonalisable perturbation of it and computing the non-diagonalisable limit of its eigenvectors. As an example, I will show how to compute a subset of the spectrum of the eclectic spin chain by computing the appropriate limit of the Bethe states of a twisted su(3) spin chain. -------- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. Link emailed on Tuesday.

The generalized Wilson loop operator interpolating between the supersymmetric and the ordinary Wilson loop in $\mathcal{N}$=4 SYM theory provides an interesting example of renormalization group flow on a line defect: the scalar coupling parameter $\zeta$ has a non-trivial beta function and may be viewed as a running coupling constant in a 1d defect QFT. We continue the study of this operator, generalizing previous results for the beta function and Wilson loop expectation value to the case of an arbitrary representation of the gauge group and away from the planar limit. Focusing on the scalar ladder limit where the generalized Wilson loop reduces to a purely scalar line operator in a free adjoint theory, and specializing to the case of the rank $k$ symmetric representation of $SU(N)$, we also study a certain "semiclassical" limit where $k$ is taken to infinity with $k \zeta^2$ fixed. This limit can be conveniently studied using a 1d defect QFT representation in terms of path integral over $N$ commuting 1d bosons. Using this representation, we compute the beta function and circular loop expectation value in the large $k$ limit, and use it to derive constraints on the structure of the beta function for general representation. We discuss the corresponding 1d RG flow and comment on the consistency of the results with the 1d defect version of the F-theorem. ----------- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.

Since time immemorial, mankind has responded to stories. Recently, anthropologists and scientists—from Joseph Campbell to Randy Olsen—have tasked themselves with exploring the fundamental structures of stories, uncovering story types and patterns that repeat across the centuries. Film-makers and novelists have used these to tremendous effect, harnessing the power of the hero's journey to create unforgettable narratives. Yet scientists, by contrast, have been slow on the uptake. In this event, Prof. Alison Woollard talks about the science of storytelling and storytelling in science. A Royal Institution Trustee who gave the iconic Christmas Lectures, she touches on the neuroscience of learning, the role of story in primitive cultures and the structure of story. Moreover, she argues that story is a crucial ingredient in communicating scientific discovery, which we hold as a core belief at the London Institute. The event is in our 2nd-floor seminar room in the Royal Institution. After introductory drinks at 5:00, the talk starts at 5.30, followed by drinks and discussion afterwards. RSVP at smc@lims.ac.uk.

It is well understood how the 2d free scalar CFT emerges from 3d Chern-Simons theory with chiral boundary conditions. Adapting a recent proposal of Costello and Stefanski, I will show how bosonic string theory can be obtained from this description by coupling to a dynamical Beltrami differential in the 3d theory. In particular, I will show how this Beltrami differential restores worldsheet diffeomorphism and Weyl invariance in the 2d theory, and recover the Polyakov action explicitly. By rewriting the theory in the BV formalism, I will show how the bc ghost system arises from the 3d perspective. Finally, if there is sufficient time, I will provide the 3d realization of vertex operators. This talk is based on work in progress with Kevin Costello and Bogdan Stefanski. ----------- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.

Following the recent work of Eberhardt, Gaberdiel and Gopakumar, exact comparison between various quantities living on the two sides of the AdS/CFT duality has become a possibility. The goal of this talk will be to extend the existing holographic dictionary to include some non-perturbative vacua on both sides. I will start by reviewing the original, purely closed-string setup, giving arguments that string theory on AdS3 x S3 x T4 with minimal k=1 NS-NS flux is exactly dual to the symmetric-product orbifold CFT with the T4 as the seed. I will then construct various D-branes of this string theory and calculate their associated cylinder amplitudes. We will observe that these amplitudes match with the cylinder correlators of certain boundary states of the dual CFT, thus suggesting a direct correspondence between these boundary conditions. I will also show that the disk amplitudes of these D-branes localise to those points in the worldsheet moduli space where the worldsheet disk holomorphically covers the spacetime disk. This talk is based on https://arxiv.org/abs/2110.05509. ---- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.

To many people, the phrase “the theory of everything” conjures memories of the Oscar-winning film about the life and science of Prof. Stephen Hawking. Yet the quest referred to in that title goes back much further. It is nothing less than the search for the holy grail of science: an elegant unified theory, encompassing all matter, forces and space-time itself. It stretches from Galileo and Newton, via Einstein and Dirac, to the most recent advances in superstring theory. In this event, Prof. Yang-Hui He presents the story as a dance of discovery between data, physics and mathematics, each anticipating the other’s moves. They have all taken the lead at different times, yet for many today, including Prof. He, the guiding principle is the rigour and beauty of mathematics. It is fitting that this event is held at the Royal Institution, where Faraday uncovered the principles of electromagnetism. These inspired Maxwell's equations, a key component of any unifying theory.

We will have a new edition of the London Integrability Journal Club Gong Show, with six 10+5 mins talks by: Meer Ashwinkumar, Kavli Inst. Tokyo, "Three-dimensional WZW model and the R-matrix of the Yangian". Carlos Bercini, ICTP-SAIFR, "The Wilson Loop - Large Spin OPE Dictionary". Aleix Gimenez-Grau, DESY, "Bootstrapping holographic defect correlators". Himanshu Khanchandani, Princeton Univ., "CFT in AdS and Gross-Neveu BCFT". Levente Pristyak, Budapest Univ., "Current operators in the XYZ model". Xinyu Zhang, DESY, "Hidden symmetry in 4d N=2 quiver gauge theory". Abstracts and schedule can be found on the LIJC website, integrability-london.weebly.com . If you are not registered, please email Andrea Cavaglia at KCL for the Zoom link.

Live Tutorial. This lecture provides an introduction to duality symmetries in string theory. String theory was originally formulated as a theory of strings propagating in space time with interactions governed by the string coupling constant g. Scattering amplitudes for small g were constructed as a perturbation theory in g. Five consistent supersymmetric string theories were found, all in 10 spacetime dimensions with five distinct perturbation theories. This left many questions unanswered, such as why there should be five apparently consistent quantum theories of gravity and what happens to these theories as the coupling constant is increased. Such questions were answered by the developments in the mid-1990s that have been called the 2nd superstring revolution. Dualities proved to be the key to uncovering the non-perturbative structure of superstring theory and in particular its strong coupling behaviour. When g is large, one can analyse the theory as a perturbation theory in 1/g and seek a "dual theory" with coupling constant g' whose perturbative expansion in g' matches the behaviour of the original theory as a perturbation theory in 1/g on identifying g'=1/g. In some cases the dual theory is again a string theory, which might be a different string theory from the original one. In other cases, the dual theory isn't a string theory at all, but a new theory - M-theory. This leads to a picture in which all 5 string theories are related by dualities and so are all seen as different limits of M-theory. Duality transformation provide new symmetries of string/M theory and T,S and U-dualities. Remarkably, the theory that emerges is no longer just a theory of strings but one which includes both strings and branes which are higher dimensional extended objects. As the branes are related to strings by duality symmetries, they should be regarded as being on the same footing as the strings and of equal importance. The lecture explores all of these issues and discusses some examples. Please register at https://lonti.weebly.com/registration.html to receive joining instructions for this live session which will be held via Zoom.

The Euler-scale power-law asymptotics of space-time correlation functions in many-body systems, quantum and classical, can be obtained by projecting the observables onto the hydrodynamic modes admitted by the model and state. This is the Boltzmann-Gibbs principle; it works for integrable and non-integrable models alike. However, certain observables, such as some order parameters in thermal of generalised Gibbs ensembles, do not couple to any hydrodynamic mode: the Boltzmann-Gibbs principle gives zero. I will explain how hydrodynamics can still give the leading exponential decay of order parameter correlation functions. With the examples of the quantum XX chain and the sine-Gordon model, I will explain how large deviations of the spin and U(1) current fluctuations are related to such exponential decay. Exact predictions are given by the ballistic fluctuation theory based on generalised hydrodynamics. In the XX model, this is in agreement with results obtained previously by a more involved Fredholm determinant analysis and other techniques, and even gives a new formula for a parameter regime not hitherto studied. In the sine-Gordon model, these are new results, inaccessible by other techniques. Works in collaboration with Giuseppe Del Vecchio Del Vecchio, and Márton Kormos. ---- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.

Lonti Autumn 2021 Series: Lecture 4. Live Tutorial. Please register at https://lonti.weebly.com/registration.html to receive joining instructions for this live session which will be held via Zoom. Gauge theories are ubiquitous in theoretical physics, not to mention that the standard model is one. It is therefore of utmost importance to know what the observables of these theories are, quantities that can be calculated and measured. I start with a long discussion based on the most familiar gauge theory, Maxwell's electromagnetism, where a lot of computations can be done explicitly. I then take the lessons from that to non-abelian gauge theories. The observables covered are local, Wilson loops, and briefly 't Hooft loops and surface operators.

This lecture provides an introduction to duality symmetries in string theory. String theory was originally formulated as a theory of strings propagating in space time with interactions governed by the string coupling constant g. Scattering amplitudes for small g were constructed as a perturbation theory in g. Five consistent supersymmetric string theories were found, all in 10 spacetime dimensions with five distinct perturbation theories. This left many questions unanswered, such as why there should be five apparently consistent quantum theories of gravity and what happens to these theories as the coupling constant is increased. Such questions were answered by the developments in the mid-1990s that have been called the 2nd superstring revolution. Dualities proved to be the key to uncovering the non-perturbative structure of superstring theory and in particular its strong coupling behaviour. When g is large, one can analyse the theory as a perturbation theory in 1/g and seek a "dual theory" with coupling constant g' whose perturbative expansion in g' matches the behaviour of the original theory as a perturbation theory in 1/g on identifying g'=1/g. In some cases the dual theory is again a string theory, which might be a different string theory from the original one. In other cases, the dual theory isn't a string theory at all, but a new theory - M-theory. This leads to a picture in which all 5 string theories are related by dualities and so are all seen as different limits of M-theory. Duality transformation provide new symmetries of string/M theory and T,S and U-dualities. Remarkably, the theory that emerges is no longer just a theory of strings but one which includes both strings and branes which are higher dimensional extended objects. As the branes are related to strings by duality symmetries, they should be regarded as being on the same footing as the strings and of equal importance. The lecture explores all of these issues and discusses some examples. Please register at https://lonti.weebly.com/registration.html to receive joining instructions for this live session which will be held via Zoom. The lecture is available here: https://youtube.com/playlist?list=PLlva4MroG-KHsP0WGLxRk9ZWsmAHUklMT

Several years ago, a new gauge theory called four-dimensional Chern-Simons was introduced by Costello in an attempt to explain the integrability of various two-dimensional models using techniques in gauge theory. My work focuses on the use of four-dimensional Chern-Simons to explain the integrability of two-dimensional sigma models. I will begin by reviewing the construction of the Wess-Zumino-Witten (WZW) model as the boundary theory of three-dimensional Chern-Simons theory as was introduced by Moore and Seiberg. This will allow me to introduce the analogous construction of Costello and Yamazaki, in which two-dimensional sigma models appear as theories on defects in four-dimensional Chern-Simons. This naturally leads to a discussion of my work in which I construct a large class of gauged sigma models by coupling together two four-dimensional Chern-Simons theories. I will argue that the structure of four-dimensional Chern-Simons suggests that these models are integrable and finish by constructing the gauged WZW model and conformal Toda theories. This talk is based on: https://arxiv.org/abs/2109.08101. ---- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.

Lonti Autumn 2021 Series: Lecture 3. Live Tutorial. Please register at https://lonti.weebly.com/registration.html to receive joining instructions for this live session which will be held via Zoom. CPT-symmetry is a fundamental symmetry of nature that is respected by all physical processes. It consists of a consecutive reversal of time (T), reflection of space at an arbitrary point (Parity P) and a charge conjugation that replaces particles by antiparticles. I briefly discuss the role P T -symmetry plays in quantum mechanics and how it may be utilised for a consistent formulation of non-Hermitian theories. For a relativistic quantum field theory the CPT-theorem provides the general framework for the validity of this symmetry to occur, by stating that the CPT-symmetry is equivalent to a strong reflection and a simultaneous Hermitian conjugation. In this lecture I will prove the theory in the framework of a Lagrangian quantum field theory for spin 0, 1 and spin 1/2 Dirac fields, by first identifying the separate transformation and a subsequent combination. Subsequently these transformations are used to identify the behaviour of various interaction terms under their action. I conclude by commenting on the experimental observations of CP-symmetry violation in the neutral K-meson decay.

Lonti Autumn 2021 Series: Lecture 4. Release of Recorded Lecture. Available at https://youtu.be/JLbuSnt2OyA. Gauge theories are ubiquitous in theoretical physics, not to mention that the standard model is one. It is therefore of utmost importance to know what the observables of these theories are, quantities that can be calculated and measured. I start with a long discussion based on the most familiar gauge theory, Maxwell's electromagnetism, where a lot of computations can be done explicitly. I then take the lessons from that to non-abelian gauge theories. The observables covered are local, Wilson loops, and briefly 't Hooft loops and surface operators.

t.b.a. ---- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.

Lonti Autumn 2021 Series: Lecture 2. Live Tutorial. Please register at https://lonti.weebly.com/registration.html to receive joining instructions for this live session which will be held via Zoom. Abstract: In this lecture, we present a few elementary facts about Fermi surfaces, then discuss how to find interesting ``non-Fermi liquids'' via the AdS/CFT correspondence. We study different backgrounds (e.g. AdS, BTZ, and Reissner-Nordstrom), and the wave-equation of probe fields on top of these geometries. We discuss how to compute boundary two-point functions by solving the bulk equations and then explore the results.

Lonti Autumn 2021 Series: Lecture 3. Release of Recorded Lecture. Available at https://youtu.be/zABaRs1Ghmw CPT-symmetry is a fundamental symmetry of nature that is respected by all physical processes. It consists of a consecutive reversal of time (T), reflection of space at an arbitrary point (Parity P) and a charge conjugation that replaces particles by antiparticles. I briefly discuss the role P T -symmetry plays in quantum mechanics and how it may be utilised for a consistent formulation of non-Hermitian theories. For a relativistic quantum field theory the CPT-theorem provides the general framework for the validity of this symmetry to occur, by stating that the CPT-symmetry is equivalent to a strong reflection and a simultaneous Hermitian conjugation. In this lecture I will prove the theory in the framework of a Lagrangian quantum field theory for spin 0, 1 and spin 1/2 Dirac fields, by first identifying the separate transformation and a subsequent combination. Subsequently these transformations are used to identify the behaviour of various interaction terms under their action. I conclude by commenting on the experimental observations of CP-symmetry violation in the neutral K-meson decay.

I will describe my work with N.Nekrasov on supersymmetric interfaces in gauge theories in the context of the Bethe/gauge correspondence. These interfaces, viewed as operators on the Hilbert space, give linear maps between spaces of SUSY vacua, understood mathematically as generalized cohomology theories of the Higgs branch. A natural class of interfaces are SUSY Janus interfaces for masses, with the corresponding cohomological maps being either the stable envelopes or the chamber R-matrices (both due to Maulik-Okounkov and Aganagic-Okounkov). Thus, such interfaces (and their collisions) can be used to define actions of the spectrum generating algebras (such as Yangians) on the “gauge” side of the Bethe/gauge correspondence, i.e., in QFT. Further applications and possible generalizations will be mentioned as well. ------------------- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.