Supersymmetric fluid dynamics

Recently, Navier-Stokes equations have been derived from the duality between the black branes and a conformal fluid on the boundary of anti-de Sitter ₅. Nevertheless, the full correspondence has to be established between solutions of supergravity in anti-de Sitter ₅ and supersymmetric field theories on the boundary. That prompts the construction of Navier-Stokes equations for a supersymmetric fluid. In the framework of rigid supersymmetry, there are several possibilities and we propose one candidate. We deduce the equations of motion in two ways: both from the divergenceless 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.