# Dissipative hydrodynamics in superspace

## TL;DR

This paper develops a superspace-based effective field theory for relativistic hydrodynamics in charged thermal systems, ensuring symmetry constraints and fluctuation-dissipation relations are naturally incorporated.

## Contribution

It introduces a novel superspace formalism for constructing hydrodynamic effective actions that simplifies symmetry implementation and extends previous theoretical frameworks.

## Key findings

- The effective theory respects the Kubo-Martin-Schwinger condition.
- Green's functions in the theory satisfy the fluctuation-dissipation theorem.
- The formalism provides a more efficient way to impose symmetries in hydrodynamic models.

## 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.