Abstract
Abstract 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.
Highlights
The study of two-dimensional conformal field theories in terms of their minimal model description, their Landau-Ginzburg phase or as gauged linear sigma-models has proven to be very useful [1, 2]
The study has had a profound impact on our understanding of compact Calabi-Yau manifolds and mirror symmetry, and it has had interesting applications in the field of singular manifolds and toric varieties
The extension of this study to include theories with non-compact targets, and in particular non-compact Calabi-Yau manifolds is very interesting. It is a natural generalization from the perspective of studying Calabi-Yau manifolds locally, or from the viewpoint of understanding holography in curved non-compact spaces that asymptotically have a linear dilaton profile [4, 5]. This field has already given rise to many results including a study of the map between deformations of the geometry and the spectrum of non-compact conformal field theories [6,7,8,9,10], mirror symmetry for non-compact Gepner models, as well as an intriguing relation between orbifolds in asymptotically linear dilaton spaces and flat space toric orbifolds [10]
Summary
The study of two-dimensional conformal field theories in terms of their minimal model description, their Landau-Ginzburg phase or as gauged linear sigma-models has proven to be very useful [1, 2]. It is a natural generalization from the perspective of studying Calabi-Yau manifolds locally, or from the viewpoint of understanding holography in curved non-compact spaces that asymptotically have a linear dilaton profile [4, 5] This field has already given rise to many results including a study of the map between deformations of the geometry and the spectrum of non-compact conformal field theories [6,7,8,9,10], mirror symmetry for non-compact Gepner models, as well as an intriguing relation between orbifolds in asymptotically linear dilaton spaces and flat space toric orbifolds [10]. Conformal field theory elliptic genera provide a natural way to complete the product of two mock modular forms. We apply this general reasoning to non-compact Gepner models and their orbifolds in.
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