Superconformal Field Theories for Compact Manifolds with Spin(7) Holonomy
Ralph Blumenhagen, Volker Braun
TL;DR
This paper constructs superconformal field theories for Spin(7) holonomy manifolds, relating them to Calabi-Yau quotients, and compares geometric and Gepner model results.
Contribution
It introduces a new construction of superconformal field theories for Spin(7) manifolds using Gepner models and analyzes their topological invariants.
Findings
Betti numbers determined for the models
Discrepancy found between Gepner and geometric results
Extension of methods from G_2 to Spin(7) manifolds
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.
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