Relativistic fluid mechanics, Kahler manifolds and supersymmetry

TL;DR

This paper reformulates relativistic fluid mechanics using Kahler manifolds and complex potentials, revealing an infinite set of conserved currents and extending the theory to include supersymmetry with additional fields.

Contribution

It introduces a Kahler manifold-based reformulation of relativistic fluid mechanics and explores its supersymmetric extension, highlighting new conserved currents and algebraic structures.

Findings

Infinite conserved currents in the vacuum sector.

Explicit expressions for current and density.

Supersymmetric extension with additional fields.

Abstract

We propose an alternative for the Clebsch decomposition of currents in fluid mechanics, in terms of complex potentials taking values in a Kahler manifold. We reformulate classical relativistic fluid mechanics in terms of these complex potentials and rederive the existence of an infinite set of conserved currents. We perform a canonical analysis to find the explicit form of the algebra of conserved charges. The Kahler-space formulation of the theory has a natural supersymmetric extension in 4-D space-time. It contains a conserved current, but also a number of additional fields complicating the interpretation. Nevertheless, we show that an infinite set of conserved currents emerges in the vacuum sector of the additional fields. This sector can therefore be identified with a regime of supersymmetric fluid mechanics. Explicit expressions for the current and the density are obtained.