Axial-Vector Duality as a Mirror Symmetry

TL;DR

This paper demonstrates that in certain supersymmetric gauged Wess-Zumino-Witten models, vector and axial gaugings are mirror duals, revealing an equivalence of superconformal theories and implications for space-time singularities.

Contribution

It establishes the mirror symmetry between vector and axial gauged models in $N=2$ supersymmetric contexts, showing their equivalence as superconformal field theories.

Findings

Vector gauged models are transformed into axial gauged models via mirror symmetry.

The models are equivalent as $N=(2,2)$ superconformal field theories.

Implications for space-time singularities in string backgrounds are discussed.

Abstract

We study $N=2$ supersymmetric $SU(2)/U(1)$ and $SL(2,R)/U(1)$ gauged Wess-Zumino-Witten models. It is shown that the vector gauged model is transformed to the axial gauged model by a mirror transformation. Therefore the vector gauged model and the axial gauged model are equivalent as $N=(2,2)$ superconformal field theories. In the $SL(2,R)/U(1)$ model, it is known that axial-vector duality relates a background with a singularity to that without a singularity. Implications of the equivalence of these two models to space-time singularities are discussed.