Abstract
We discuss string compactifications on manifolds with SU( n) holonomy by making use of representation theories of extended superconformal algebras. In particular, string compactification on K 3 surfaces is discussed in detail. We calculate loop-space indices and show that all c = 6 superconformal field theories describe string propagation on manifolds with SU(2) holonomy. We study Gepner's models based on the tensoring of N = 2 minimal series and point out that some of these models are identified as orbifolds. We also discuss c = 9 superconformal field theories and their relation to Calabi-Yau manifolds.
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