Abstract
Recently Witten proposed to consider the elliptic genus in N = 2 superconformal field theory to understand the relation between N = 2 minimal models and Landau-Ginzburg theories. In this paper we first discuss the basic properties satisfied by elliptic genera in N = 2 theories. These properties are confirmed by some fundamental class of examples. Then we introduce a generic procedure to compute the elliptic genera of a particular class of orbifold theories, i.e. the ones orbifoldized by e 2 πiJ 0 in the Neveu-Schwarz sector. This enables us to calculate the elliptic genera for Landau-Ginzburg orbifolds. When the Landau-Ginzburg orbifolds allow an interpretation as target manifolds with SU ( N) holonomy we can compare the expressions with the ones obtained by orbifoldizing tensor products of N = 2 minimal models. We also give sigma model expressions of the elliptic genera for manifolds of SU ( N) holomony.
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