MIRROR SYMMETRY AS A POISSON-LIE T-DUALITY

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 on the N=2 super-Virasoro algebra generators acts as a mirror symmetry: 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 again acts as a mirror symmetry.