LANDAU-GINZBURG ORBIFOLDS, MIRROR SYMMETRY AND THE ELLIPTIC GENUS

We compute the elliptic genus for arbitrary two-dimensional N = 2 Land au-Ginzburg orbifolds. This is used to search for possible mirror pair s of such models. We show that if two Landau-Ginzburg models are conju gate to each other in a certain sense, then to every orbifold of the f irst 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 an ti-chiral rings interchanged. These orbifolds thus constitute a possib le mirror pair. Furthermore, new pairs of conjugate models may be obta ined by taking the product of old ones. We also give a sufficient (and possibly necessary) condition for two models to be conjugate, and sho w that it is satisfied by the mirror pairs proposed by one of the auth ors and Hubsch.