Comments on HKT supersymmetric sigma models and their Hamiltonian reduction

TL;DR

This paper derives simplified expressions for supercharges in HKT supersymmetric sigma models using complex notation, explores their relation to hypercomplex structures, and discusses Hamiltonian reduction leading to quasicomplex models.

Contribution

It introduces new simple formulas for supercharges in HKT models and connects Hamiltonian reduction to quasicomplex sigma models.

Findings

New expressions for supercharges using complex notation

Identification of hypercomplex structure role in supercharges

Hamiltonian reduction yields quasicomplex sigma models

Abstract

Using complex notation, we present new simple expressions for two pairs of complex supercharges in HKT supersymmetric sigma models. The second pair of supercharges depends on the holomorphic antisymmetric "hypercomplex structure" tensor which plays the same role for the HKT models as the complex structure tensor for the Kaehler models. When the Hamiltonian and supercharges commute with the momenta conjugate to the imaginary parts of the complex coordinates, one can perform a Hamiltonian reduction. The models thus obtained represent a special class of quasicomplex sigma models introduced recently by Ivanov and Smilga.