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We prove the equivalence of the SL(2,R)/U(1) Kazama-Suzuki model, which is afermionic generalization of the 2d Black Hole, and N=2 Liouville theory. Weshow that this duality is an example of mirror symmetry. The essential part ofthe derivation is to realize the fermionic 2d Black Hole as the low energylimit of a gauged linear sigma-model. Liouville theory is obtained by dualizingthe charged scalar fields and taking into account the vortex-instanton effects,as proposed recently in non-dilatonic models. The gauged linear sigma-model westudy has many useful generalizations which we briefly discuss. In particular,we show how to construct a variety of dilatonic superstring backgrounds whichgeneralize the fermionic 2d Black Hole and admit a mirror description in termsof Toda-like theories.Comment: 48 pages, latex2e, 1 eps figur

Duality of the fermionic 2d black hole and N = 2 Liouville theory as mirror symmetry