Hydrodynamics with higher-form symmetries from black holes

The symmetries of a state of matter determine the structure of the hydrodynamic theory that governs its dynamical properties over long length and time scales. As such, a hydrodynamic theory gives a universal description of macroscopic properties of states of matter that is to some extent independent of the state's microscopic details. A simple example is the theory of fluid dynamics.

However, the macroscopic dynamical properties of a state are still sensitive to its microscopic details, through the parameters in the hydrodynamic theory (for example, the viscosity in fluid dynamics). While changing the nature of the microscopic degrees of freedom and their interactions will alter these parameters, their values cannot be completely arbitrary if the microscopic theory is a consistent quantum mechanical theory.

This project will involve the study of theories with generalised global symmetries and associated higher-form conservation laws. We will focus on a class of examples that are under theoretical control even at the microscopic level - strongly interacting quantum field theories with gravitational descriptions. First we will determine what theories of hydrodynamics emerge macroscopically - we expect this will provide an equivalence between certain black hole solutions of Einstein's equations and hydrodynamic theories such as those of charged plasmas or viscoelastic solids. In this class of examples, the parameters in the hydrodynamic theories will be related to properties of black holes. We will then examine if and how general properties of black holes provide restrictions on the values of hydrodynamic parameters and whether these can be interpreted as requirements of microscopic consistency conditions. Conversely, we will determine if and how consistency conditions of the hydrodynamic theory (such as causality) can be used to classify the types of black holes that have a sensible hydrodynamic limit.