Superconformal Field Theories for Compact Manifolds with Spin(7) Holonomy

Abstract

We present a construction of superconformal field theories for manifolds with Spin(7) holonomy. Geometrically these models correspond to the realization of Spin(7) manifolds as anti-holomorphic quotients of Calabi-Yau fourfolds. Describing the fourfolds as Gepner models and requiring anomaly cancellation we determine the resulting Betti numbers of the Spin(7) superconformal field theory. As in the G_2 case, we find that the Gepner model and the geometric result disagree.

16 pages, TeX, harvmac, refs. added

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