Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-02-06
Nucl.Phys.B853:739-759,2011
Physics
High Energy Physics
High Energy Physics - Theory
19 pages, references added, expanded discussion on relating torsion to phenomenology, published version
Scientific paper
10.1016/j.nuclphysb.2011.08.006
We interpret heterotic M-theory in terms of h-cobordism, that is the eleven-manifold is a product of the ten-manifold times an interval is translated into a statement that the former is a cobordism of the latter which is a homtopy equivalence. In the non-simply connected case, which is important for model building, the interpretation is then in terms of s-cobordism, so that the cobordism is a simple-homotopy equivalence. This gives constraints on the possible cobordisms depending on the fundamental groups and hence provides a characterization of possible compactification manifolds using the Whitehead group-- a quotient of algebraic K-theory of the integral group ring of the fundamental group-- and a distinguished element, the Whitehead torsion. We also consider the effect on the dynamics via diffeomorphisms and general dimensional reduction, and comment on the effect on F-theory compactifications.
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