Compactification of D=11 supergravity on spaces of exceptional holonomy

TL;DR

This paper explores how eleven-dimensional supergravity can be compactified on special holonomy manifolds, revealing potential links to heterotic string theories and emphasizing the role of specific Calabi-Yau spaces.

Contribution

It demonstrates the compactification of D=11 supergravity on manifolds with exceptional holonomy and suggests equivalences with heterotic string compactifications in lower dimensions.

Findings

Lower-dimensional theories are Maxwell/Einstein supergravities.

Evidence of equivalence with heterotic string compactifications.

Calabi-Yau manifolds with specific Hodge numbers are crucial.

Abstract

We investigate the compactification of D=11 supergravity to D=5,4,3, on compact manifolds of holonomy $SU(3)$ (Calabi-Yau), $G_2$, and $Spin(7)$, respectively, making use of examples of the latter two cases found recently by Joyce. In each case the lower dimensional theory is a Maxwell/Einstein supergravity theory. We find evidence for an equivalence, in certain cases, with heterotic string compactifications from D=10 to D=5,4,3, on compact manifolds of holonomy $SU(2)$ ($K_3\times S^1$), $SU(3)$, and $G_2$, respectively. Calabi-Yau manifolds with Hodge numbers $h_{1,1}=h_{1,2}=19$ play a significant role in the proposed equivalences.