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

@article{Hori2001DualityOT, title={Duality of the Fermionic 2d Black Hole and N = 2 Liouville Theory as Mirror Symmetry}, author={Kentaro Hori and Anton Kapustin}, journal={Journal of High Energy Physics}, year={2001}, volume={2001}, pages={045-045} }

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…

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