Hitchin's equations and M-theory phenomenology

Phenomenological compactifications of M-theory involve seven-manifolds with G(2) holonomy and various singularities. Here we study local geometries with such singularities, by thinking of them as compactifications of 7d supersymmetric Yang-Mills theory on a three-manifold Q(3). We give a general discussion of compactifications of 7d Yang-Mills theory in terms of Higgs bundles on Q(3). We show that they can be constructed using spectral covers, which are Lagrangian branes with a flat connection in the cotangent bundle T*Q(3). We explain the dictionary with ALE fibrations over Q(3) and conjecture that these configurations have G(2) holonomy. We further develop tools to study the low energy effective theory of such a model. We show that the naive massless spectrum is corrected by instanton effects. Taking the instanton effects into account, we find that the massless spectrum and many of the interactions can be computed with Morse theoretic methods. (C) 2011 Elsevier B.V. All rights reserved.