In this talk I will present the novel developments pertaining the the thermodynamics of the XXZ spin-1/2 chain. I will describe the analysis allowing one to prove several features related to the behaviour of the Heisenberg-Ising (or XXZ) spin-1/2 chain at finite temperature. It has been argued in the literature that the per-site free energy or the correlation length admit integral representations whose integrands are expressed in terms of solutions of non-linear integral equations. The derivations of such representations rested on various unproven conjectures such as the existence of a real, non-degenerate, maximal in modulus Eigenvalue of the quantum transfer matrix, the existence and uniqueness of the solutions to the auxiliary non-linear integral equations in the infinite Trotter limit. I will show how these conjectures can be proven in a rigorous setting for temperatures high enough. The result of these analyses allowed one to observe that a subset of sub-dominant Eigenvalues of the quantum transfer matrix admits a large temperature asymptotic expansion.

I will review asymptotic charges in electromagnetism and explain why they are physical. Then I will review BMS charges in asymptotically flat spacetimes and show that there are in fact magnetic analogues of BMS charges that had been overlooked in the literature. I will comment on the implications of these newly found charges.

Since the 1980s, the study of invariants of 3-dimensional manifolds has benefited from the connections between topology, physics and number theory. Recently, a new topological invariant has been discovered: the homological block (also known as the half-index of certain 3d N=2 theories). When the 3-manifold is a Seifert manifold given by a negative-definite plumbing the homological block turned out to be related to false theta functions and characters of logarithmic VOA's. In this talk I describe the role of quantum modular forms, false and mock theta functions in the study of the topology of 3-manifolds. The talk is based on the article 1809.10148 and work in progress with Cheng, Chun, Feigin, Gukov, and Harrison.

In this talk, we discuss conformal field theories in two dimensions (2d CFTs) and aspects of the theory of modular forms. Physical considerations lead us to study two extensions to the theory of modular forms: modular forms for GL2(Z) that are defined on the double half-plane (in distinction to SL2(Z) modular forms defined on the upper half-plane), and L-functions for modular forms with poles *within* the fundamental domain. We introduce both concepts, and discuss their consistency, both with each other and with the physical considerations which led to them. Finally, we note that very similar physical considerations may apply to finite-temperature path integrals for generic QFTs in higher dimensions, and comment on possible consequences of this.

Novel insights into quantum gravity in asymptotically flat spacetimes evolving around soft theorems in scattering amplitudes, memory effects and asymptotic symmetries hint at an underlying holographic structure of Minkowski spacetime: information about 4D quantum gravity might be encoded in a 2D CFT on the celestial sphere at the conformal boundary of Minkowski spacetime. I will discuss recent progress on this attempted formulation of a flat space holography focusing on the 4D S-matrix which takes the form of a 2D correlator on the celestial sphere in a conformal basis. I will discuss how celestial conformal symmetry is generated by "conformally soft" gravitons and how insertions of the BMS supertranslation current in a correlator gives rise to the celestial analogue of Weinberg's soft graviton theorem.

Solitons and breathers are localized solutions of integrable systems that can be viewed as "particles'' of complex statistical objects called soliton and breather gases. In view of the growing evidence of their ubiquity in fluids and nonlinear optical media these ``integrable'' gases present fundamental interest for nonlinear physics. We develop nonlinear spectral theory of breather and soliton gases by considering a special, thermodynamic type limit of the nonlinear dispersion relations for multi-phase (finite-gap) solutions of the focusing nonlinear Schrödinger (fNLS) equation. A number of concrete examples of breather and soliton gases are considered, demonstrating efficacy of the developed general theory and also having some interesting implications. In particular, the statistical properties of a special kind of soliton gas, that we term the bound state soliton condensate, reveal a remarkable connection with the nonlinear stage of modulational instability. This is joint work with Alex Tovbis (Central Florida).

I will review recent progress in our understanding of light-ray operators in abstract CFTs. Light-ray operators first appeared in QCD and were later studied in N=4 Super Yang-Mills theory and holography by Hofman and Maldacena. More recently, they attracted new interest due to an important role played by the averaged null energy condition (ANEC) operator in various contexts. However, it is only during the last few years it became possible to start developing a more general theory of light-ray operators. I will explain a nonperturbative, convergent operator product expansion (OPE) for null-integrated operators on the same null plane in a CFT. I will discuss its application to energy-energy correlators in N=4 Super Yang-Mills theory.

Certain quantum field theories possess generalized global symmetries; just as ordinary global symmetries enforce the conversation of particle number, generalized global symmetries enforce the conservation of extended objects, such as strings. I will review this symmetry principle and argue that it governs the long-distance physics of conventional 4d electromagnetism, where the strings in question are magnetic field lines. I will then apply it to construct a novel effective theory for the description of strongly magnetized plasmas. One potential application of this new effective theory is to astrophysical pulsars, which are thought to be surrounded by strong magnetic fields as well as a high density of charged particles; the resulting zero temperature system is highly nonlinear. At leading order in derivatives our new effective theory agrees with the standard treatment in terms of ``force-free electrodynamics''. The inclusion of higher derivative terms however generically results in new and potentially observationally relevant effects, such as electric fields that accelerate charges to high energies along magnetic field lines. If time permits I will describe some recent work towards describing such energetic charges in terms of bosonization along magnetic field lines.

In this talk, I will describe new mathematical structures in the low-energy expansion of one-loop string amplitudes. The insertion of external states on the open- and closed-string worldsheets requires integration over punctures on a cylinder boundary and a torus, respectively. Suitable bases of such integrals will be shown to obey simple first-order differential equations in the modular parameter of the surface. These differential equations will be exploited to perform the integrals order by order in the inverse string tension, similar to modern strategies for dimensionally regulated Feynman integrals. Our method manifests the appearance of iterated integrals over holomorphic Eisenstein series in the low-energy expansion. Moreover, infinite families of Laplace equations can be generated for the modular forms in closed-string low-energy expansions.

I discuss the dependence of supersymmetric partition functions on continuous parameters for the flavour symmetry group. In the presence of the 't Hooft anomalies, the supersymmetric Ward identities imply that the partition function computed in the Wess-Zumino gauge has a non-holomorphic dependence on the flavour parameters. I show this explicitly for a large class of 4d N=1 partition functions on half-BPS four manifolds. I propose a new expression for the partition functions on M3 x S1, which differs from earlier holomorphic results by a non-holomorphic Casimir pre-factor.

Costello, Witten, and Yamazaki have recently proposed a new description of quantum integrable systems using a variant of Chern-Simons theory defined on the product of a two dimensional real manifold and a Riemann surface. I'll review their work, and show how to extend it to describe integrable systems with boundary. In particular I'll discuss how it can be used to generate solutions of the boundary Yang-Baxter equation, and how to realise twisted Yangians in the theory. If there is enough time I will explore the result of applying this construction when the Riemann surface is chosen to be a torus.

A large class of 4d SCFTs can be engineered by wrapping a stack of M5-branes on a compact space, possibly with defects. ‘t Hooft anomalies are crucial observables for such theories, which often do not admit any known Lagrangian description. Building on the seminal work of Freed, Harvey, Minasian, Moore, we develop systematic tools for extracting the ‘t Hooft anomalies of a geometrically engineered 4d theory using anomaly inflow from the M-theory bulk. We exemplify our tools by studying a class of setups with M5-branes probing a C^2/Z_2 singularity. We argue that these setups define 4d SCFTs which are dual to a class of AdS_5 solutions­—first discussed by Gauntlett, Martelli, Sparks, Waldram—whose field theory interpretation has been a longstanding puzzle.

This is a two day meeting, please see the website for details. www.tinyurl.com/kcldef19 Registration is required as King's has a new policy on attendance. Supported by the LMS and the IoP

AdS/CFT provides a consistent non-perturbative definition of quantum gravity in asymptotically AdS space. Black holes should correspond to ensembles of states in the boundary field theory. By analyzing the superconformal index of 4d N=4 SU(N) Super-Yang-Mills, with the help of a new Bethe Ansatz type formula, we are able to exactly reproduce the Bekenstein-Hawking entropy of BPS black holes in AdS5 x S5. The large N limit exhibits many competing contributions and Stokes phenomena, hinting at new physics.

In flat space, four point scattering amplitudes at weak coupling can be fully determined from Lorentz symmetry, unitarity and causality. The resulting scattering amplitude depends on model details only through coupling constants and the particle content of the theory. I will show how the analogous story works in the case of inflationary fluctuations. We found explicit expressions for inflationary three and four-point functions, whose shapes depend on the field content of the theory, and do not depend on the specific inflationary model, as long as the fluctuations minimally break de Sitter symmetry. This ``cosmological bootstrap” is a first step towards classifying all possible shapes of primordial non-gaussianity, which can be searched for in experimental data.

A four-dimensional abelian gauge theory can be coupled to a 3d CFT with a U(1) symmetry living on a boundary. This coupling gives rise to a continuous family of boundary conformal field theories (BCFTs) parametrized by the gauge coupling \tau and by the choice of the CFT in the decoupling limit. Upon performing an Electric-Magnetic duality in the bulk and going to the decoupling limit in the new frame, one finds a different 3d CFT on the boundary, related to the original one by Witten's SL(2, Z) action. In particular the cusps on the real \tau axis correspond to the 3d gauging of the original CFT. We study general properties of this family of BCFTs. We show how to express bulk one and two-point functions, and the hemisphere free-energy, in terms of the two-point functions of the boundary electric and magnetic currents. Finally, upon assuming particle-vortex duality (and its fermionic version), we show how to turn this machinery into a powerful computational tool to study 3d gauge theories.

We show that supersymmetry is anomalous in N = 1 superconformal quantum field theories (SCFTs) with an anomalous R-symmetry. This anomaly was originally found in holographic theories: here we show that this anomaly is present in general and demonstrate it for the massless superconformal Wess-Zumino model via a one loop computation of four-point functions of two supercurrents with either R-currents. In fact, the Wess-Zumino consistency conditions together with the standard R-symmetry anomaly imply the existence of the anomaly. We outline the implications of this anomaly.

KCL TPPC Seminar

KCL TPPC Seminar Abstract: Black hole (BH) mergers can be viewed as cosmological “scattering experiments” resulting in an excited BH, which then decays to its ground state by emitting gravitational waves (GW). I will present general arguments, based on fundamental physics principles, as to why we should expect additional quantum ringdown modes to those predicted by general relativity. Then, I will discuss the spectrum of the predicted ringdown modes, the resulting emitted GW and the prospects for their detection in LIGO/VIRGO.

TBA