Perfect fluid equations with N=1,2 Schrodinger supersymmetry

TL;DR

This paper develops superconformal extensions of perfect fluid equations with N=1,2 Schrodinger supersymmetry, introducing anticommuting fields as superpartners for fluid variables and analyzing their conserved charges.

Contribution

It constructs superconformal fluid equations with N=1,2 Schrodinger supersymmetry using Hamiltonian and Lagrangian formalisms, including the interpretation of anticommuting variables as vorticity potentials.

Findings

Constructed superconformal fluid equations with N=1,2 supersymmetry.

Derived the full set of conserved charges for these supersymmetric fluids.

Interpreted anticommuting variables as fluid vorticity potentials.

Abstract

Superconformal extensions of the perfect fluid equations, which realize $N=1,2$ Schrodinger superalgebra, are constructed within the Hamiltonian formalism. They are built by introducing real (for $N=1$) or complex (for $N=2$) anticommuting field variables as superpartners for the density and velocity of a fluid. The full set of conserved charges associated with the $N=1,2$ Schrodinger superalgebra is constructed. Within the Lagrangian formalism, when the Clebsch decomposition for the velocity vector field is used, the anticommuting variables can be interpreted as potentials parameterizing fluid's vorticity.