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arXiv · hep-th/9401029

Landau-Ginzburg Orbifolds, Mirror Symmetry and the Elliptic Genus

P. Berglund·M. Henningson
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Abstract

We compute the elliptic genus for arbitrary two dimensional $N=2$ Landau-Ginzburg orbifolds. This is used to search for possible mirror pairs of such models. We show that if two Landau-Ginzburg models are conjugate to each other in a certain sense, then to every orbifold of the first theory corresponds an orbifold of the second theory with the same elliptic genus (up to a sign) and with the roles of the chiral and anti-chiral rings interchanged. These orbifolds thus constitute a possible mirror pair. Furthermore, new pairs of conjugate models may be obtained by taking the product of old ones. We also give a sufficient (and possibly necessary) condition for two models to be conjugate, and show that it is satisfied by the mirror pairs proposed by one of the authors and~Hübsch.

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P. Berglund, M. Henningson. 1994-01-07. Landau-Ginzburg Orbifolds, Mirror Symmetry and the Elliptic Genus. https://doi.org/10.1016/0550-3213(94)00389-v

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