Multiple spin structures in higher-dimensional physics

Details Multiple spin structures in higher-dimensional physics Multiple spin structures in higher-dimensional physics

Dec 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996cqgra..13.3175m&link_type=abstract

Classical and Quantum Gravity, Volume 13, Issue 12, pp. 3175-3182 (1996).

Mathematics

Logic

Scientific paper

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 0264-9381/13/12/008/img1 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.

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