Comments on M Theory Dynamics on G2 Holonomy Manifolds

TL;DR

This paper investigates M-theory dynamics on G2 holonomy manifolds, analyzing their moduli spaces, superpotentials, and effects of symmetry breaking, with implications for membrane instantons and gauge symmetry.

Contribution

It provides a detailed analysis of G2 manifolds as quotients of the spin bundle over S^3, including moduli space structure, superpotentials, and the impact of Wilson lines, highlighting new geometric and physical insights.

Findings

Smooth interpolation between three classical geometries.

Explicit superpotentials for M-theory on these quotients.

Insights into membrane instanton effects and gauge symmetry breaking.

Abstract

We study the dynamics of M-theory on G2 holonomy manifolds, and consider in detail the manifolds realized as the quotient of the spin bundle over S^3 by discrete groups. We analyse, in particular, the class of quotients where the triality symmetry is broken. We study the structure of the moduli space, construct its defining equations and show that three different types of classical geometries are interpolated smoothly. We derive the N=1 superpotentials of M-theory on the quotients and comment on the membrane instanton physics. Finally, we turn on Wilson lines that break gauge symmetry and discuss some of the implications.