Landau-Ginzburg Orbifolds, Mirror Symmetry and the Elliptic Genus

Details Landau-Ginzburg Orbifolds, Mirror Symmetry and the Elliptic Genus Landau-Ginzburg Orbifolds, Mirror Symmetry and the Elliptic Genus

1994-01-07

arxiv.org/abs/hep-th/9401029v1

Nucl.Phys. B433 (1995) 311-332

Physics

High Energy Physics

High Energy Physics - Theory

p.22, IASSNS-HEP-93/92, use harvmac

Scientific paper

10.1016/0550-3213(94)00389-V

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~H\"ubsch.

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