Multiple spin structures in higher-dimensional physics

Abstract

On many Calabi-Yau manifolds there is no unique way to define spinor fields. We point out that, through the usual procedure of 'embedding the spin connection in the gauge algebra', this non-uniqueness can have major (and invariably unwelcome) consequences for the corresponding string theories. For example, topological effects can lead to ambiguities in the breaking of E8 and even to a loss of the supersymmetry that originally motivated consideration of Calabi-Yau manifolds themselves. We argue that, in string theory, attention should be concentrated on non-simply-connected Calabi-Yau manifolds which nevertheless have a unique spin structure, of which the Tian-Yau manifold is an example. © 1996 IOP Publishing Ltd.