Week 17.10.2022 – 23.10.2022

We will describe the duality between two integrable systems: the 2D Sine-Gordon model and the 2D Thirring model. We will spend some time describing the classical and quantum Sine-Gordon model, in particular its spectrum, S-matrices and underlying quantum-group symmetry. We will then present the duality with the Thirring model as originally stated by Coleman and refined in subsequent literature. All the basic elements will be provided without relying on too many pre-requisites beyond standard graduate-level quantum field theory. The notes comprise a series of exercises.

Fracton phases are characterized by their elementary excitations having restricted mobility, and have recently been of relevance in several subjects, from quantum information to thermalization, from gravity to elasticity. In the context of hydrodynamics it has been shown theoretically, and confirmed experimentally, that such restricted mobility leads to novel emergent scaling laws. In this talk, I will introduce a framework to describe the hydrodynamics of fractons and predict such scaling laws, with particular focus on systems with conserved dipole and momentum. This hydrodynamics turns out to have rather exotic properties, owing to the fact that dipole conservation leads to a non-trivial extension of spacetime symmetries. After developing an effective theory approach that allows accounting for fluctuations, I will show that such theory contains relevant nonlinearities that lead to the emergence of stochastic non-Gaussian universality classes, even in three spatial dimensions, thus constituting a breakdown of its local hydrodynamic description.

I will discuss recent developments in the characterisation of asymptotic states in asymptotically flat gravity, and the central role played by BMS fluxes in connection to soft graviton theorems. As a result of these new ideas, I will show that the subleading soft graviton theorem including loop effects is the Ward identity associated with superrotations symmetries. We will conclude that BMS symmetries are genuine symmetries of the gravitational S-matrix beyond the classical regime.

Quantum annealers are near-term adiabatic quantum computing devices that are already of significant size. In this talk I discuss how they can be used as laboratories to implement genuine tunnelling in Quantum Field Theories. I also discuss how they can be used to embed and train a general neural network in a quantum annealer without introducing any classical element in training. This approach opens a novel avenue for the quantum training of general machine learning models which can incorporate virtually limitless and changing training data. The talk will include a pedagogical introduction to quantum annealing.

I will discuss the large N behavior of partition functions of the ABJM theory on compact Euclidean manifolds. I will pay particular attention to the S^3 free energy and the topologically twisted index for which I will present closed form expressions valid to all orders in the large N expansion. These results have important implications for holography and the microscopic entropy counting of AdS_4 black holes which I will discuss. I will also briefly discuss generalizations to other SCFTs arising from M2-branes.