Scherk-Schwarz reduction of M-theory on G2-manifolds with fluxes

TL;DR

This paper investigates the effective supergravity theories from M-theory compactified on G2-structured manifolds with fluxes, detailing the superpotential and exploring the landscape of vacua, including reductions to type IIA backgrounds.

Contribution

It provides explicit formulas for the Kaehler potential and superpotential in M-theory on G2-manifolds with fluxes, and analyzes the vacuum structure and reductions to type IIA.

Findings

Explicit supergravity expressions with fluxes and geometry

Identification of vacua in flux compactifications

Superpotentials for type IIA backgrounds derived from M-theory

Abstract

We analyse the 4-dimensional effective supergravity theories obtained from the Scherk--Schwarz reduction of M-theory on twisted 7-tori in the presence of 4-form fluxes. We implement the appropriate orbifold projection that preserves a G2-structure on the internal 7-manifold and truncates the effective field theory to an N=1, D=4 supergravity. We provide a detailed account of the effective supergravity with explicit expressions for the Kaehler potential and the superpotential in terms of the fluxes and of the geometrical data of the internal manifold. Subsequently, we explore the landscape of vacua of M-theory compactifications on twisted tori, where we emphasize the role of geometric fluxes and discuss the validity of the bottom-up approach. Finally, by reducing along isometries of the internal 7-manifold, we obtain superpotentials for the corresponding type IIA backgrounds.