Sigma Models in (4,4) Harmonic Superspace

TL;DR

This paper develops a new harmonic superspace framework for (4,4) 2D sigma models, introducing novel superfield actions, dualities, and exploring models with torsion, complex structures, and specific group manifold examples.

Contribution

It constructs a comprehensive harmonic superspace formulation for (4,4) sigma models, including new superfield actions, dual representations, and insights into models with torsion and complex structures.

Findings

Defined (4,4) harmonic superspace with two SU(2) harmonic variables.

Constructed superfield actions for (4,4) sigma models with torsion.

Established duality transformations and new off-shell representations.

Abstract

We define basics of $(4,4)\;\; 2D$ harmonic superspace with two independent sets of $SU(2)$ harmonic variables and apply it to construct new superfield actions of $(4,4)$ supersymmetric two-dimensional sigma models with torsion and mutually commuting left and right complex structures, as well as of their massive deformations. We show that the generic off-shell sigma model action is the general action of constrained analytic superfields $q^{(1,1)}$ representing twisted $N=4$ multiplets in $(4,4)$ harmonic superspace. The massive term of $q^{(1,1)}$ is shown to be unique; it generates a scalar potential the form of which is determined by the metric on the target bosonic manifold. We discuss in detail $(4,4)$ supersymmetric group manifold $SU(2)\times U(1)$ WZNW sigma model and its Liouville deformation. A deep analogy of the relevant superconformally invariant analytic superfield action to that of the improved tensor $N=2\;\;4D$ multiplet is found. We define $(4,4)$ duality transformation and find new off-shell dual representations of the previously constructed actions via {\it unconstrained} analytic $(4,4)$ superfields. The dual representation suggests some hints of how to describe $(4,4)$ models with non-commuting complex structures in the harmonic superspace.