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.

In conversation: Sir Roger Penrose, Thomas Fink & Yang-Hui He Live at the Royal Institution + Livestream Sir Roger Penrose is a mathematical physicist with the eye of an artist and the soul of a philosopher. He won the 2020 Nobel Prize in Physics for his work on the mathematical foundations of black holes. The tilings which bear his name can cover the plane in a never-repeating pattern. His work on the theory of mind suggests consciousness is a peculiarly human capability. He is a master word-smither, capable of rendering the most complex ideas clear, and his popular books have inspired a generation of physicists and laymen alike. In this event, Sir Roger joins Thomas Fink and Yang-Hui He on stage for a conversation about the man behind the science. We take a rare look into the workings of this singular mind. How does he get his ideas? Is beauty a guide to truth? What’s the basis of free will? Is AI a threat? Can art inform science? And is man different from machine? https://www.rigb.org/whats-on/events-2021/october/public-in-conversation-with-sir-roger-penrose https://lims.ac.uk/event/in-conversation-with-sir-roger-penrose/

Lonti Autumn 2021 Series: Lecture 2. Release of Recorded Lecture. Available at https://youtu.be/5IAx2ca_WU4 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.

Matrix bootstrap is a new method for the numerical study of (multi)-matrix models in the planar limit, using loop equations for moments of distribution (Ward identities and factorization of traces at infinite N). The lack of information associated with the use of only a finite number of lower moments is supplemented by the conditions of positivity of the correlation matrix. The numerical solution of loop equations and these conditions leads to inequalities for the lowest moments, which rapidly converge to exact values with an increase in the number of used moments. In our work https://arxiv.org/pdf/2108.04830.pdf, the method was tested on the example of the standard one-matrix model, as well as on the case of an ''unsolvable'' 2-matrix model with the interaction tr[A, B]^2 and with quartic potentials. We propose a significant improvement of original H. Lin's proposal for matrix bootstrap by introducing the relaxation procedure: we replace the non-convex, non-linear loop equations by convex inequalities. The results look quite convincing and matrix bootstrap seems to be an interesting alternative to the Monte Carlo method. For example, for < tr A^2 >, the precision reaches 6 digits (with modest computer resources). I will discuss the prospects for applying the method in other, physically interesting systems. --------------------- 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.

In this talk we will revisit the study of spin chains capturing the spectral problem of 4d N = 2 SCFTs in the planar limit. At one loop and in the quantum plane limit, we will discover a quasi-Hopf symmetry algebra, defined by the R-matrix read off from the superpotential. This implies that when orbifolding the N = 4 symmetry algebra down to the N = 2 one and then marginaly deforming, the broken generators are not lost, but get upgraded to quantum generators. We will also demonstrate that these chains are dynamical, in the sense that their Hamiltonian depends on a parameter which is dynamically determined along the chain. At one loop we will show how to map the holomorphic SU(3) scalar sector to a dynamical 15-vertex model, which corresponds to an RSOS model, whose adjacency graph can be read off from the gauge theory quiver/brane tiling. One scalar SU(2) sub-sector is described by an alternating nearest-neighbour Hamiltonian, while another choice of SU(2) sub-sector leads to a dynamical dilute Temperley-Lieb model. These sectors have a common vacuum state, around which the magnon dispersion relations are naturally uniformised by elliptic functions. For the example of the ℤ_{2} quiver theory we study these dynamical chains by solving the one- and two-magnon problems with the coordinate Bethe ansatz approach. --- Part of the London Integrability Journal Club. If you are a new participant, please register at integrability-london.weebly.com. The link will be emailed on Tuesday.

We will review the subject of line defects in d-dimensional Conformal Field Theories (CFTs). We discuss an exact formula governing the renormalization group flow on line defects and consider some examples involving line defects in 2,3, and 4 space-time dimensions. ---------------- 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.

This is the last appointment before September for the London Integrability Journal Club. We will have four 10+5 mins talks by: - Ilija Buric (DESY), "Defect conformal blocks from the Iwasawa decomposition" - Luigi Guerrini (U. of Parma), "A duality for the latitude Wilson loop in ABJM", -Daniele Gregori (U. of Bologna), "Integrability and cycles of deformed N=2 gauge theory" - Enrico Olivucci (Perimeter), "Hexagons in Fishnet theories: direct derivation". Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.