Supercharges in the HKT Supersymmetric Sigma Models

TL;DR

This paper constructs explicit classical and quantum supercharges in N=4 supersymmetric sigma models on HKT manifolds, linking physical models with mathematical superalgebra frameworks.

Contribution

It provides the first explicit construction of supercharges satisfying N=4 supersymmetry algebra in HKT sigma models, bridging physics and mathematics.

Findings

Supercharges satisfy N=4 supersymmetry algebra

Explicit classical and quantum formulations provided

Connection to mathematical superalgebra established

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.