Four-dimensional Effective M-theory on a Singular G_2 Manifold

TL;DR

This paper derives a four-dimensional N=1 supersymmetric theory from M-theory compactified on a singular G_2 manifold, explicitly including gauge fields at singularities and analyzing effects of fluxes and Wilson lines.

Contribution

It provides explicit formulae for the Kahler potential, gauge-kinetic function, and superpotential in this setting, and interprets orbifold blow-up as a Higgs effect, connecting to smooth G_2 spaces.

Findings

Explicit formulae for Kahler potential, gauge-kinetic function, superpotential

Orbifold blow-up described as a Higgs effect in the theory

Analysis of flux and Wilson line effects on singular loci

Abstract

We reduce M-theory on a G_2 orbifold with co-dimension four singularities, taking explicitly into account the additional gauge fields at the singularities. As a starting point, we use 11-dimensional supergravity coupled to seven-dimensional super-Yang-Mills theory, as derived in a previous paper. The resulting four-dimensional theory has N=1 supersymmetry with non-Abelian N=4 gauge theory sub-sectors. We present explicit formulae for the Kahler potential, gauge-kinetic function and superpotential. In the four-dimensional theory, blowing-up of the orbifold is described by a Higgs effect induced by continuation along D-flat directions. Using this interpretation, we show that our results are consistent with the corresponding ones obtained for smooth G_2 spaces. In addition, we consider the effects of switching on flux and Wilson lines on singular loci of the G_2 space, and we discuss the relation to N=4 SYM theory.