N=(4,4) supersymmetry and T-duality

TL;DR

This paper explores how T-duality relates different N=(4,4) supersymmetric sigma models, showing that off-shell supersymmetry can be preserved through duality transformations involving chiral, twisted chiral, and semichiral fields.

Contribution

It demonstrates the explicit duality transformation connecting off-shell N=(4,4) supersymmetric models with different superfield content and reveals the necessity of non-linear terms for supersymmetry closure in semichiral models.

Findings

T-duality relates chiral/twisted chiral models to semichiral models.

Additional non-linear terms are required for supersymmetry in semichiral models.

Supersymmetry algebra closes on-shell due to T-duality.

Abstract

A sigma model with four-dimensional target space parametrized by chiral and twisted chiral N=(2,2) superfields can be extended to N=(4,4) supersymmetry off-shell, but this is not true for a model of semichiral fields, where the N=(4,4) supersymmetry can only be realized on-shell. The two models can be related to each other by T-duality. In this paper we perform a duality transformation from a chiral and twisted chiral model with off-shell N=(4,4) supersymmetry to a semichiral model. We find that additional non-linear terms must be added to the original transformations to obtain a semichiral model with N=(4,4) supersymmetry, and that the algebra closes on-shell as a direct consequence of the T-duality.