Triangle Seminars

Abstract:
Models of random matrices can be viewed as zero-dimensional analogs of usual field theory. Despite decades of exploration, matrix models remain at the forefront of intensive research, motivated by a rich web of connections to string theory, quantum gravity, integrability, Yang-Mills theory, combinatorics, geometry and representation theory. These lectures will present a pedagogical introduction to the subject.

​Lecture 1. Motivation and basic definitions. Hermitian matrix models: Feynman rules, ribbon graphs, large N genus expansion.
Lecture 2. Reduction to eigenvalues. Large N limit, Coulomb gas approach, saddle point equations.
Lecture 3. Continuum limit of saddle point equations. Eigenvalue density and spectral curve. Examples.

Abstract:
In this talk I will explain how certain aspects of black hole physics can be understood using ideas from effective field theory. Many of the familiar notions from particle physics will play a role, including the renormalization group, universality and naturalness. In particular, I will explain why black holes naively seem like fine-tuned systems, but they are ultimately not. I will also explain how their effective description reveals a degree of universality that can be used to resum certain features of the gravitational waveform for binary mergers observed by LIGO/Virgo/Kagra.

Abstract:
Higher-spin conserved currents and charges feature prominently in integrable 2d QFTs in flat space. Motivated by the question of integrable field theories in curved space and by results of the conformal bootstrap, we will consider the consequences of higher-spin currents for QFTs in AdS2. Namely, we will show that their presence is much more constraining than in flat space in particular proving that it is impossible to preserve: (a) any higher-spin charges when deforming a massive free field by interactions, or (b) any spin-4 charges when deforming a CFT by a Virasoro primary. Along the way, we will show that in AdS one cannot `partially' conserve a higher-spin current and explain how higher-spin charges lead to integer spacing in the spectrum of primaries, and to constraints on correlation functions.

Abstract:
In this talk, I will report some progress in systematizing the correspondence between universal statistical features of 2d CFT data and pure AdS_3 quantum gravity. In particular, I will show that non-handlebodies are necessary in the sum over topologies, in order to furnish a statistical ensemble of OPE data that is compatible with both crossing symmetry and \it{typicality}, a notion familiar from the Eigenstate Thermalization Hypothesis. Using the tools of Virasoro TQFT, I will relate index contractions of random OPE coefficients to surgery operations on 3-manifolds. Combining this surgery with crossing transformations generates a large class of hyperbolic non-handlebodies in the topological expansion of 3d gravity. Based on ongoing work with Alex Belin, Scott Collier, Lorenz Eberhardt and Diego Liska.

Abstract:
The emergence of a universal pre-hydrodynamic attractor behaviour during fluid thermalisation is an important feature in the study of ultra-relativistic nuclear collisions and cold atom experiments: highly non-hydrodynamic behaviour dictated by initial conditions quickly decays towards this attractor solution, with the resulting hydrodynamic system independent of the initial state.

There are many approaches to study the emergence of this attractor. We will briefly review these approaches, then focusing on kinetic theory. Starting with the relativist Boltzmann equation in the so-called relaxation time approximation, we introduce a series of moments and their generating function, which we show solved a single PDE. We solve this PDE perturbatively for all moments, both in the small and large time approximations, and we then recover the free streaming and attractor regimes at each end via methods of analytic continuation.

Abstract:
The matter and fundamental forces in our universe are described by so-called non-abelian gauge theories, and by General Relativity. Traditionally, these theories are very different, but recent research has uncovered a remarkable correspondence - the “double copy” - that precisely relates their mathematical structure. The correspondence relates to other theoretical structures (e.g. string theory), and to an increasingly complex web of exotic field theories. In this talk, I will review the origin of the double copy and its practical applications, before discussing links with open problems in pure mathematics.

Abstract:
I will explain how the irreversibility of the renormalization group together with anomalies, including anomalies in the space of coupling constants, can be used to constrain the IR phases of defects in familiar quantum field theories. As an example, I will use these techniques to provide evidence for a conjectural "spin-flux duality" which describes how certain line operators are mapped across particle/vortex duality in 2+1d.

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https://lims.ac.uk/event/anomalies-of-defect-parameter-spaces-and-a-spin-flux-duality/

London Institute for Mathematical Sciences (LIMS),
Royal Institution.
21 Albemarle St,
London W1S 4BS, UK