M-theory compactification, fluxes and AdS_4

TL;DR

This paper explores supersymmetric solutions in M-theory with specific internal geometries, deriving conditions for fluxes and cosmological constants, and presents explicit solutions involving warped products with AdS_4.

Contribution

It derives the most general supersymmetry conditions for M-theory compactifications on SU(3) structure manifolds with fluxes and finds explicit solutions with warped geometries.

Findings

Non-vanishing cosmological constant requires different norms of internal spinors.

Explicit solutions involve warped products of a circle, nearly-Kahler manifold, and AdS_4.

Embedding solutions into heterotic M-theory is discussed.

Abstract

We analyze supersymmetric solutions of M-theory based an a seven-dimensional internal space with SU(3) structure and a four-dimensional maximally symmetric space. The most general supersymmetry conditions are derived and we show that a non-vanishing cosmological constant requires the norms of the two internal spinors to differ. We find explicit local solutions with singlet flux and the space being a warped product of a circle, a nearly-Kahler manifold and AdS_4. The embedding of solutions into heterotic M-theory is also discussed.