L2

Energy correlations characterise the energy flux through detectors at infinity produced in a collision event. In CFTs, these detectors are examples of light-ray operators and, in particular, the stress tensor operator integrated over future null infinity. In N=4 SU(N_c) SYM, we combine perturbation theory, holography, integrability, supersymmetric localisation, and modern conformal bootstrap techniques to obtain predictions for such a collider experiment at finite coupling, both at finite number of colours, and in the planar limit. In QCD, the coupling runs with the angle between detectors, and there is a transition from perturbative to non-perturbative QCD. In N=4 SYM, a similar transition occurs when the coupling is varied, which we explore quantitatively. I will describe the physics underlying this observable and some of the methods used, particularly in regimes with analytical control.

It is well known to mathematicians that there is a deep relationship between the arithmetic of algebraic varieties and their geometry.  

In recent years, there has been increasing evidence for a geometric representation of quantum chaos within Einstein's theory of general relativity. Despite the lack of a complete theoretical framework, this overview will explore various examples of this phenomenon. It will also discuss the lessons we have learned from it to address several existing puzzles in quantum gravity, such as the black hole information paradox and off-shell wormhole geometries.

Symmetry Topological Field Theories (SymTFTs) are topological field theories that encode the symmetry structure of global symmetries in terms of a theory in one higher dimension. While SymTFTs for internal (global) symmetries have been highly successful in characterizing symmetry aspects in the last few years, a corresponding framework for spacetime symmetries remains unexplored. We propose an extension of the SymTFT framework to include spacetime symmetries. In particular, we propose a SymTFT for the conformal symmetry in various spacetime dimensions. We demonstrate that certain BF-type theories, closely related to topological gravity theories, possess the correct topological operator content and boundary conditions to realize the conformal algebra of conformal field theories living on boundaries. As an application, we show how effective theories with spontaneously broken conformal symmetry can be derived from the SymTFT, and we elucidate how conformal anomalies can be reproduced in the presence of even-dimensional boundaries.
 

One of the great powers of global symmetry is its ability to constrain the possible phases of many-body quantum systems. In this talk, we will present a symmetry that enforces every symmetric model to be in a phase with a Fermi surface. This constraint is entirely non-perturbative and a strong form of symmetry-enforced gaplessness. We construct this symmetry in fermionic quantum lattice models on a $d$-dimensional Bravais lattice, and it is generated by a U(1) fermion-number symmetry and Majorana translation symmetry. The resulting symmetry group is an infinite-dimensional non-abelian Lie group closely related to the Onsager algebra. We will comment on the topology of these symmetry-enforced Fermi surfaces and the UV symmetry's relation to the IR LU(1) symmetry of ersatz Fermi liquids. (This talk is based on ongoing work with Shu-Heng Shao and Luke Kim.)

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.

Einstein’s equations are difficult to solve and if you want to compute something in holography knowing an explicit metric seems to be essential. Or is it? For some theories, observables, such as on-shell actions and free energies, are determined solely in terms of topological data, and an explicit metric is not needed. One of the key tools that has recently been used for this programme is equivariant localization, which gives a method of computing integrals on spaces with a symmetry. In this talk I will give a pedestrian introduction to equivariant localization before showing how it can be used to compute the on-shell action of 6d Romans Gauged supergravity.