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

TL;DR

This work derives the 4D ${ m N}=1$ supergravity from M-theory compactified on twisted ${ m T}^7$ with 4-form fluxes, using a Scherk--Schwarz reduction that yields a G$_2$-structure on the internal manifold. The authors provide explicit Kähler and superpotential expressions in terms of geometric data and fluxes, and analyze the vacuum structure under Jacobi constraints, showing that supersymmetric Minkowski vacua require G$_2$-holonomy while AdS$_4$ vacua require weak G$_2$-holonomy and full moduli dependence in ${ m W}$. They classify viable geometric twists into four algebra families and study their vacuum/outlook, including a detailed Type IIA reduction that reproduces known SU(3)-structure results and highlights additional quadratic couplings in the M-theory setting. The results illuminate moduli stabilization mechanisms in fluxed M-theory on G$_2$-structure manifolds, and establish a bridge to IIA descriptions, with implications for constructing controlled ${ m N}=1$ vacua in higher-dimensional theories.

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.