Mirror Symmetry as a Poisson-Lie T-Duality

TL;DR

This paper explores how Poisson-Lie T-duality acts as a mirror symmetry on N=2 super-Virasoro algebra generators in superconformal models, revealing a novel symmetry transformation in string theory.

Contribution

It demonstrates that Poisson-Lie T-duality induces mirror symmetry-like transformations on N=2 super-Virasoro generators in superconformal models, including Kazama-Suzuki models.

Findings

Poisson-Lie T-duality changes sign of U(1) current in one chirality sector.

It interchanges spin-3/2 currents between sectors.

The transformation preserves the algebra structure, acting as a mirror symmetry.

Abstract

The transformation properties of the N=2 Virasoro superalgebra generators under Poisson-Lie T-duality in (2,2)-superconformal WZNW and Kazama-Suzuki models is considered. It is shown that Poisson-Lie T-duality acts on the N=2 super-Virasoro algebra generators as a mirror symmetry does: it unchanges the generators from one of the chirality sectors while in another chirality sector it changes the sign of U(1) current and interchanges spin-3/2 currents. We discuss Kazama-Suzuki models generalization of this transformation and show that Poisson-Lie T-duality acts as a mirror symmetry also.