Duality of the Fermionic 2d Black Hole and N=2 Liouville Theory as Mirror Symmetry

TL;DR

This paper establishes a duality between the fermionic 2d Black Hole model and N=2 Liouville theory, demonstrating it as an instance of mirror symmetry through a detailed derivation involving gauged linear sigma-models.

Contribution

It proves the equivalence of the fermionic 2d Black Hole and N=2 Liouville theory, revealing a new example of mirror symmetry and exploring generalizations for superstring backgrounds.

Findings

Fermionic 2d Black Hole is dual to N=2 Liouville theory.

Mirror symmetry is realized between these models.

Constructs generalized dilatonic superstring backgrounds.

Abstract

We prove the equivalence of the SL(2,R)/U(1) Kazama-Suzuki model, which is a fermionic generalization of the 2d Black Hole, and N=2 Liouville theory. We show that this duality is an example of mirror symmetry. The essential part of the derivation is to realize the fermionic 2d Black Hole as the low energy limit of a gauged linear sigma-model. Liouville theory is obtained by dualizing the charged scalar fields and taking into account the vortex-instanton effects, as proposed recently in non-dilatonic models. The gauged linear sigma-model we study has many useful generalizations which we briefly discuss. In particular, we show how to construct a variety of dilatonic superstring backgrounds which generalize the fermionic 2d Black Hole and admit a mirror description in terms of Toda-like theories.