On the Quantum Poisson-Lie T-duality and Mirror Symmetry

TL;DR

This paper explores quantum Poisson-Lie T-duality in N=2 superconformal models, revealing its role as a mirror symmetry that interchanges algebraic structures and proposing a generalization to Kazama-Suzuki models.

Contribution

It derives the transformation rules for super-Kac-Moody currents under quantum Poisson-Lie T-duality and demonstrates its action as a mirror symmetry in superconformal models, including a generalization to Kazama-Suzuki models.

Findings

Quantum Poisson-Lie T-duality acts as a mirror symmetry on N=2 super-Virasoro algebra.

Transformation rules for super-Kac-Moody currents are explicitly derived.

The duality is generalized to Kazama-Suzuki models, showing similar mirror symmetry behavior.

Abstract

Poisson-Lie T-duality in quantum N=2 superconformal WZNW models is considered. The Poisson-Lie T-duality transformation rules of the super-Kac-Moody algebra currents are found from the conjecture that, as in the classical case, the quantum Poisson-Lie T-duality is given by an automorphism which interchanges the isotropic subalgebras of the underlying Manin triple of the model. It is shown that quantum Poisson-Lie T-duality acts on the generators of the N=2 super-Virasoro algebra of the quantum models as a mirror symmetry acts: in one of the chirality sectors it is trivial transformation while in another chirality sector it changes the sign of the U(1) current and interchanges the spin-3/2 currents. A generalization of Poisson-Lie T-duality for the Kazama-Suzuki models is proposed. It is shown that quantum Poisson-Lie T-duality acts in these models as a mirror symmetry also.