Off-shell (4,4) supersymmetric sigma models with torsion in harmonic superspace

TL;DR

This paper develops a supersymmetric off-shell formulation for a broad class of 2D (4,4) sigma models with torsion, complex structures, and gauge invariance, using harmonic superspace with two sets of SU(2) harmonics.

Contribution

It introduces a new harmonic superspace approach for (4,4) sigma models with torsion, including nonabelian gauge invariance and auxiliary fields, and explores complex structure non-commutativity.

Findings

Formulation of off-shell (4,4) sigma models with torsion in harmonic superspace.

Identification of gauge invariance and auxiliary fields in the models.

Explicit demonstration of non-commuting complex structures in specific models.

Abstract

We present a manifestly supersymmetric off-shell formulation of a wide class of $(4,4)$ $2D$ sigma models with torsion and both commuting and non-commuting left and right complex structures in the harmonic superspace with a double set of $SU(2)$ harmonic variables. The distinguishing features of the relevant superfield action are: (i) in general nonabelian and nonlinear gauge invariance ensuring a correct number of physical degrees of freedom; (ii) an infinite tower of auxiliary fields. This action is derived from the most general one by imposing the integrability condition which follows from the commutativity of the left and right analyticity-preserving harmonic derivatives. For a particular class of such models we explicitly demonstrate the non-commutativity of complex structures on the bosonic target.