Supersymmetric Deformations of G_2 Manifolds from Higher-Order Corrections to String and M-Theory

TL;DR

This paper derives and solves first-order correction equations for G_2 holonomy manifolds in string and M-theory, revealing how higher-order effects deform supersymmetric compactifications.

Contribution

It provides explicit first-order correction formulas for G_2 manifolds and solves these equations for various known cohomogeneity-one metrics.

Findings

Corrected metrics explicitly obtained for known G_2 structures

First-order corrections expressed in terms of calibrating 3-form

Deformation away from special holonomy due to higher-order effects

Abstract

The equations of 10 or 11 dimensional supergravity admit supersymmetric compactifications on 7-manifolds of $G_2$ holonomy, but these supergravity vacua are deformed away from special holonomy by the higher-order corrections of string or M-theory. We find simple expressions for the first-order corrections to the Einstein and Killing spinor equations in terms of the calibrating 3-form of the leading-order G_2-holonomy background. We thus obtain, and solve explicitly, systems of first-order equations describing the corrected metrics for most of the known classes of cohomogeneity-one 7-metrics with G_2 structures