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 G2 case, we find that the Gepner model and the geometric result disagree.
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