Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-06-21
Nucl.Phys.B414:191-212,1994
Physics
High Energy Physics
High Energy Physics - Theory
24 pages, harvmac (citation corrected, reference added)
Scientific paper
10.1016/0550-3213(94)90428-6
Recently Witten proposed to consider 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, {\it i.e.\/} the ones orbifoldized by $e^{2\pi iJ_0}$ 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 $SU(N)$ holonomy.
Kawai Toshiya
Yamada Yasuhiko
Yang Sung-Kil
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