Departamento de Fisica, Universidad de Santiago de Chile
Casilla 307, Santiago 2, Chile
E-mail:  mplyushc@lauca.usach.cl

Nonlinear Supersymmetry

Abstract:
The nonlinear supersymmetry is characterized by a polynomial superalgebra resembling the nonlinear finite W-algebras. As a usual linear supersymmetry,  it can also be formulated starting from the classical level but, unlike the former one, its quantization faces the problem of quantum anomaly. We give a complete classification of the 1D classical systems with nonlinear supersymmetry and describe a special class of such systems with holomorphic supercharges that admits the anomaly-free quantization and turns out to be related to the quasi-exactly solvable systems. The generalization for the case of a  2D system describing the charged spin-1/2 particle in external magnetic field allows us to reveal a universal algebraic structure underlying the holomorphic nonlinear supersymmetry and  establish  its relation to the nonlinear supersymmetry with non-holomorphic supercharges. We show  that the essential difference of the 2D holomorphic nonlinear supersymmetry from the 1D case consists in appearance of the central charge entering nontrivially into the superalgebra.