Dissipative hydrodynamics in superspace

TL;DR

This work develops a Schwinger-Keldysh effective field theory for relativistic hydrodynamics in a thermal background using a superspace formalism. It identifies and implements doubled SK and KMS symmetries, including a topological sector, to derive a consistent effective action whose variations reproduce the doubled Ward identities and constitutive relations. The framework yields fluctuation-dissipation relations and incorporates noise through an a-type sector, all while maintaining CPT/KMS consistency through a two-sector (SK and KMS) superspace structure. The approach provides a bridge between existing SK hydrodynamics formalisms and topological/cohomological perspectives, with explicit derivative expansion and a path toward incorporating anomalies and holographic connections.

Abstract

We construct a Schwinger-Keldysh effective field theory for relativistic hydrodynamics for charged matter in a thermal background using a superspace formalism. Superspace allows us to efficiently impose the symmetries of the problem and to obtain a simple expression for the effective action. We show that the theory we obtain is compatible with the Kubo-Martin-Schwinger condition, which in turn implies that Green's functions obey the fluctuation-dissipation theorem. Our approach complements and extends existing formulations found in the literature.