Metric symmetries and spin asymmetries of Ricci-flat Riemannian manifolds

摘要

The Calabi-Yau and Joyce manifolds used in string and M-theory compactifications have no continuous groups of isometries, but they often have nontrivial discrete (actually finite) isometry groups. Discrete isometries of nonsimply connected Riemannian manifolds do not necessarily map spin structures into themselves, however; thus, inconsistencies are possible if a spin connection is used to construct the gauge vacuum. We consider this problem in detail and show how it may be avoided.