Relating gauge gravity to string theory through obstruction

Abstract

In this article we provide a more detailed account of the geometry and topology of the composite bundle formalism introduced by Tresguerres (2002 Phys. Rev. D 66 064025) to accommodate gravitation as a gauge theory. In the first half of the article we identify a global structure required by the composite construction which not only exposes how the ordinary frame and tangent bundle expected in general relativity arise but provides the link or connection between these ordinary bundles and the gauge bundles of the composite bundle construction. In the second half of the article we discuss implications of this method of constructing gravity as a fiber bundle for the global structure of spacetime. We find that the underlying manifold of the composite bundle construction is expected to admit, not only a spin structure but also a string structure. As a consequence of our work we are able to extend past work on global structures of physically reasonable spacetime manifolds. It has been shown that in four spacetime dimensions, that if an oriented, Lorentzian, four dimensional manifold is stably casual that it is parallizable, and hence admits a spin structure which allows for chiral spinors. We may now add to this that such a manifold also admits a string structure.