Supercharges in the HKT Supersymmetric Sigma Models

Abstract

We construct explicitly classical and quantum supercharges satisfying the standard N = 4 supersymmetry algebra in the supersymmetric sigma models describing the motion over HKT (hyper-Kaehler with torsion) manifolds. One member of the family of superalgebras thus obtained is equivalent to the superalgebra derived and formulated earlier in the purely mathematical framework.