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

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

2001-04-24

arxiv.org/abs/hep-th/0104202v2

JHEP 0108:045,2001

Physics

High Energy Physics

High Energy Physics - Theory

48 pages, latex2e, 1 eps figure

Scientific paper

10.1088/1126-6708/2001/08/045

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.

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