Hydrodynamics with higher-form symmetries from black holes

物质状态的对称性决定了流体力学理论的结构，而流体力学理论支配着物质在长尺度和时间尺度上的动力学性质。因此，流体力学理论给出了物质状态的宏观性质的普遍描述，在某种程度上独立于状态的微观细节。一个简单的例子是流体动力学理论，然而，通过流体动力学理论中的参数（例如，流体动力学中的粘度），状态的宏观动力学性质仍然对它的微观细节敏感。虽然改变微观自由度的性质和它们之间的相互作用会改变这些参数，但如果微观理论是一个自洽的量子力学理论，它们的值就不可能是完全任意的。这个项目将涉及对具有广义全局对称性和相关的高阶守恒律的理论的研究。我们将集中讨论一类即使在微观水平上也处于理论控制之下的例子--具有引力描述的强相互作用量子场论。首先，我们将确定宏观上出现的流体力学理论-我们希望这将提供爱因斯坦方程的某些黑洞解与流体力学理论（如带电等离子体或粘弹性固体）之间的等价性。在这类例子中，流体力学理论中的参数将与黑洞的性质有关。然后，我们将研究黑洞的一般性质是否以及如何对流体动力学参数的值提供限制，以及这些是否可以解释为微观一致性条件的要求。相反，我们将确定流体力学理论的一致性条件（如因果关系）是否以及如何用于对具有合理流体力学极限的黑洞类型进行分类。

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.