Constraints on heterotic M-theory from s-cobordism

TL;DR

This paper uses concepts from algebraic topology, specifically s-cobordism and Whitehead torsion, to analyze constraints on heterotic M-theory compactifications, especially in non-simply connected cases relevant for model building.

Contribution

It introduces a topological framework based on s-cobordism and Whitehead groups to characterize possible heterotic M-theory compactification manifolds.

Findings

Constraints depend on the fundamental group and Whitehead torsion.

Provides a classification scheme for compactification manifolds.

Discusses implications for F-theory and dimensional reduction.

Abstract

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.