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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TLDR
An exact conformal field theory describing a black hole in two-dimensional space-time is found as an SL(2,{ital openR})/U(1) gauged Wess-Zumino-Witten model, which should be regarded as an analog of the extreme Reissner-Nordstroem black hole of four-dimensional general relativity.
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