Supersymmetric Fluid Dynamics

TL;DR

This paper explores the formulation of supersymmetric Navier-Stokes equations within the AdS/CFT correspondence, aiming to connect supergravity solutions with supersymmetric boundary field theories.

Contribution

It proposes a candidate supersymmetric Navier-Stokes equation and derives its form using two different methods, advancing the understanding of supersymmetric fluid dynamics.

Findings

Derived supersymmetric Navier-Stokes equations from energy-momentum tensor conditions

Provided a complete component expansion of the supersymmetric fluid equations

Initiated preliminary analysis of the physical implications of the supersymmetric fluid

Abstract

Recently Navier-Stokes (NS) equations have been derived from the duality between the black branes and a conformal fluid on the boundary of AdS_5. Nevertheless, the full correspondence has to be established between solutions of supergravity in AdS_5 and supersymmetric field theories on the boundary. That prompts the construction of NS equations for a supersymmetric fluid. In the framework of rigid susy, there are several possibilities and we propose one candidate. We deduce the equations of motion in two ways: both from the divergenless condition on the energy-momentum tensor and by a suitable parametrization of the auxiliary fields. We give the complete component expansion and a very preliminary analysis of the physics of this supersymmetric fluid.