Classification and moduli Kähler potentials ofG2manifolds

Abstract

Compact manifolds of ${G}_{2}$ holonomy may be constructed by dividing a seven-torus by some discrete symmetry group and then blowing up the singularities of the resulting orbifold. We classify possible group elements that may be used in this construction and use this classification to find a set of possible orbifold groups. We then derive the moduli K\"ahler potential for M-theory on the resulting class of ${G}_{2}$ manifolds with blown-up codimension four singularities.