New Compactifications of Eleven Dimensional Supergravity

TL;DR

This paper develops new consistent ansatze for eleven-dimensional supergravity compactifications, rederives known solutions, and discovers novel solutions including a stretched AdS_5×CP^3 and an Euclidean AdS_2×H^2×S^7.

Contribution

It introduces new compactification ansatze using canonical forms and presents novel solutions in eleven-dimensional supergravity.

Findings

Rederived known squashed, stretched, and Englert solutions.

Discovered a new AdS_5×CP^3 solution with stretched CP^3.

Found a new Euclidean AdS_2×H^2×S^7 solution.

Abstract

Using canonical forms on S^7, viewed as an SU(2) bundle over S^4, we introduce consistent ansatze for the 4-form field strength of eleven-dimensional supergravity and rederive the known squashed, stretched, and the Englert solutions. Further, by rewriting the metric of S^7 as a U(1) bundle over CP^3, we present yet more general ansatze. As a result, we find a new compactifying solution of the type AdS_5\times CP^3, where CP^3 is stretched along its S^2 fiber. We also find a new solution of AdS_2\times H^2\times S^7 type in Euclidean space.