Perfect fluid equations with N=1,2 Schrodinger supersymmetry

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.

arXiv comment1+15 pages; v2: appendix, comments and references added, typos corrected

References in corpus (20)

• Gravity duals for non-relativistic CFTs
• Gravity & Hydrodynamics: Lectures on the fluid-gravity correspondence
• Schr"odinger invariance and space-time symmetries
• Perfect Fluid Theory and its Extensions
• On Schrödinger superalgebras
• Field-dependent symmetries of a non-relativistic fluid model
• Supersymmetric Fluid Mechanics
• The Maximal Kinematical Invariance Group of Fluid Dynamics and Explosion-Implosion Duality
• Non-relativistic conformal symmetries in fluid mechanics
• Supersymmetric extensions of Schrödinger-invariance
• Remark on quantum mechanics with N=2 Schrodinger supersymmetry
• Supersymmetric Polytropic Gas Dynamics
• Integrable Supersymmetric Fluid Mechanics from Superstrings
• Schrödinger symmetry: a historical review
• The group-theoretic approach to perfect fluid equations with conformal symmetry
• Equations of fluid dynamics with the l-conformal Galilei symmetry
• On non-equilibrium physics and string theory
• Hamiltonian formulation for perfect fluid equations with the l-conformal Galilei symmetry
• Lagrangian formulation for perfect fluid equations with the l-conformal Galilei symmetry
• Perfect fluid dynamics with conformal Newton-Hooke symmetries