Complex Structures, Duality, and WZW-Models in Extended Superspace

TL;DR

This paper explores complex structures in dual target spaces, proves integrability conditions for certain supersymmetric systems, and introduces a new superspace formulation for the WZW-model on SU(2)×U(1).

Contribution

It establishes the complex structure on dual spaces, proves integrability of specific structures in N=(2,2) systems, and develops a novel superspace formulation for the WZW-model.

Findings

Complex structure on dual of complex target space identified.

Proved integrability of the space orthogonal to the kernel of commutator of complex structures.

Introduced a new N=2 superspace formulation for the SU(2)×U(1) WZW-model.

Abstract

We find the complex structure on the dual of a complex target space. For $N=(2,2)$ systems, we prove that the space orthogonal to the kernel of the commutator of the left and right complex structures is {\em always} integrable, and hence the kernel is parametrized by chiral and twisted chiral superfield coordinates. We then analyze the particular case of $SU(2)\times SU(2)$, and are led to a new $N=2$ superspace formulation of the $SU(2)\times U(1)$ WZW-model.