OFF-SHELL (4,4) SUPERSYMMETRIC SIGMA MODELS WITH TORSION AS GAUGE THEORIES IN HARMONIC SUPERSPACE

TL;DR

This paper develops a comprehensive off-shell formulation for a broad class of (4,4) two-dimensional sigma models with torsion, non-commuting complex structures, and gauge invariance, using harmonic superspace techniques.

Contribution

It generalizes the harmonic superspace approach to include torsion and non-commuting complex structures in (4,4) sigma models, introducing gauge invariance and auxiliary fields.

Findings

Explicit off-shell description of (4,4) sigma models with torsion

Demonstration of non-commutativity of complex structures

Presence of an infinite tower of auxiliary fields

Abstract

Starting from the action of $(4,4)$ $2D$ twisted multiplets in the harmonic superspace with a double set of $SU(2)$ harmonic variables, we present its generalization which provides an off-shell description of a wide class of $(4,4)$ sigma models with torsion and non-commuting left and right complex structures. The distinguishing features of the action constructed are: (i) a nonabelian and in general nonlinear gauge invariance ensuring a correct number of physical degrees of freedom; (ii) an infinite tower of auxiliary fields. For a particular class of such models we explicitly demonstrate the non-commutativity of complex structures on the bosonic target.