$SU(2)\times SU(2)$ harmonic superspace and (4,4) sigma models with torsion

TL;DR

This paper reviews a supersymmetric off-shell formulation of torsionful (4,4) 2D sigma models using harmonic superspace with double SU(2) variables, covering models with commuting and non-commuting complex structures.

Contribution

It introduces a manifestly supersymmetric harmonic superspace approach to (4,4) sigma models with torsion, including massive deformations and complex structure variations.

Findings

Unified harmonic superspace formulation for (4,4) sigma models

Inclusion of models with non-commuting complex structures

Description of massive deformations within the framework

Abstract

We review a manifestly supersymmetric off-shell formulation of a wide class of torsionful $(4,4)$ $2D$ sigma models and their massive deformations in the harmonic superspace with a double set of $SU(2)$ harmonic variables. Sigma models with both commuting and non-commuting left and right complex structures are treated.