Perfect fluid equations with nonrelativistic conformal supersymmetries

TL;DR

This paper extends the construction of perfect fluid equations to include nonrelativistic conformal supersymmetries, specifically N=2 conformal Newton-Hooke and N=1 l-conformal Galilei superalgebras, within a Hamiltonian framework.

Contribution

It develops supersymmetric fluid models for new nonrelativistic conformal superalgebras and constructs their conserved charges and Lagrangian descriptions.

Findings

Constructed supersymmetric fluid models with N=2 and N=1 supersymmetries.

Derived the full set of conserved charges for these models.

Discussed subtleties in constructing N=2 l-conformal Galilei supersymmetric fluids.

Abstract

Our recent result on the construction of perfect fluid equations with N=1,2 Schr\"odinger supersymmetry [Mod. Phys. Lett. A 41 (2026) 2550214] is extended to accommodate nonrelativistic conformal supersymmetries of other types. Two cases are considered in detail, which include the N=2 conformal Newton-Hooke superalgebra and N=1 l-conformal Galilei superalgebra with arbitrary half-integer parameter l. Supersymmetric fluid models are built within the Hamiltonian framework by introducing real (for N=1) or complex (for N=2) anticommuting field variables as superpartners for the density and velocity. For both the cases the full set of conserved charges associated with the superalgebras is constructed and the Lagrangian description is given. Subtleties with the construction of perfect fluid equations with N=2 l-conformal Galilei supersymmetry are discussed as well.