Off-Shell Formulation of N=2 Non-Linear Sigma-Models

TL;DR

This paper develops an off-shell formulation for N=2 non-linear sigma-models in two dimensions, identifying the fundamental superfields and applying the framework to specific WZW models.

Contribution

It demonstrates that all (2,2) sigma-models can be described using chiral, twisted chiral, and semi-chiral superfields, providing explicit potentials for key examples.

Findings

All (2,2) models can be formulated with these superfields.

Explicit potentials are derived for SU(2) x U(1) and SU(2) x SU(2) models.

Different complex structures lead to different superfield descriptions.

Abstract

We study d=2, N=(2,2) non-linear sigma-models in (2,2) superspace. By analyzing the most general constraints on a superfield, we show that through an appropriate choice of coordinates, there are no other superfields than chiral, twisted chiral and semi-chiral ones. We study the resulting sigma-models and we speculate on the possibility that all (2,2) non-linear sigma-models can be described using these fields. We apply the results to two examples: the SU(2) x U(1) and the SU(2) x SU(2) WZW model. Pending upon the choice of complex structures, the former can be described in terms of either one semi-chiral multiplet or a chiral and a twisted chiral multiplet. The latter is formulated in terms of one semi-chiral and one twisted chiral multiplet. For both cases we obtain the potential explicitely.