Four-Dimensional Einstein Yang-Mills De Sitter Gravity From Eleven Dimensions

TL;DR

This paper derives a four-dimensional de Sitter gravity model coupled with SU(2) Yang-Mills fields from eleven-dimensional supergravity through a consistent Kaluza-Klein reduction on a hyperbolic 7-space, enabling uplift of solutions to higher dimensions.

Contribution

It presents an explicit reduction ansatz for obtaining 4D de Sitter gravity with Yang-Mills fields from 11D supergravity, including new embeddings of dS_2 and dS_3.

Findings

Derived D=4 de Sitter gravity coupled to SU(2) Yang-Mills from D=11 supergravity.

Constructed explicit uplift ansatz for solutions to eleven dimensions.

Embedded dS_3 in D=6 supergravity and dS_2 in M-theory.

Abstract

We obtain D=4 de Sitter gravity coupled to SU(2) Yang-Mills gauge fields from an explicit and consistent truncation of D=11 supergravity via Kaluza-Klein dimensional reduction on a non-compact space. The ``internal'' space is a smooth hyperbolic 7-space (H^7) written as a foliation of two 3-spheres, on which the SU(2) Yang-Mills fields reside. The positive cosmological constant is completely fixed by the SU(2) gauge coupling constant. The explicit reduction ansatz enables us to lift any of the D=4 solutions to D=11. In particular, we obtain dS_2 in M-theory, where the nine-dimensional transverse space is an H^7 bundle over S^2. We also obtain a new smooth embedding of dS_3 in D=6 supergravity.