Topological sigma models & dissipative hydrodynamics

TL;DR

This paper develops a universal effective theory for relativistic thermal fluctuations using topological and symmetry principles, applicable to dissipative hydrodynamics, and demonstrates its consistency with fundamental thermodynamic laws.

Contribution

It introduces a novel Schwinger-Keldysh effective framework incorporating topological supersymmetry and entropy symmetry for relativistic fluids.

Findings

Effective action satisfies a generalized fluctuation-dissipation theorem.

Ensures a local form of the second law of thermodynamics.

Applicable to non-linear viscous fluids.

Abstract

We outline a universal Schwinger-Keldysh effective theory which describes macroscopic thermal fluctuations of a relativistic field theory. The basic ingredients of our construction are three: a doubling of degrees of freedom, an emergent abelian symmetry associated with entropy, and a topological (BRST) supersymmetry imposing fluctuation-dissipation theorem. We illustrate these ideas for a non-linear viscous fluid, and demonstrate that the resulting effective action obeys a generalized fluctuation-dissipation theorem, which guarantees a local form of the second law.