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Elliptic Genera of Non-compact Gepner Models and Mirror Symmetry

We consider tensor products of N=2 minimal models and non-compact conformal field theories with N=2 superconformal symmetry, and their orbifolds. The elliptic genera of these models give rise to a large and interesting class of real Jacobi forms. The tensor product of conformal field theories leads to a natural product on the space of completed mock modular forms. We exhibit families of non-compact mirror pairs of orbifold models with c=9 and show explicitly the equality of elliptic genera, including contributions from the long multiplet sector. The Liouville and cigar deformed elliptic genera transform into each other under the mirror transformation.