Perfect fluid equations with nonrelativistic conformal supersymmetries

Abstract

Our recent result on the construction of perfect fluid equations with N=1,2 Schrödinger 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.