D-Brane Probes of G2 Holonomy Manifolds

The concept of the D-brane probe provides the link between gauge theory and geometry. It has proven to be one of the most important ideas among recent developments in string theory, shedding new light on strong coupling gauge theory dualities, providing a physical interpretation of previously obscure algebraic-geometric constructions, and resulting in examples of the AdS/CFT correspondence with increasingly realistic gauge and matter content. The purpose of this letter is to describe some results extending this enterprise to D2-brane probes of noncompact manifolds of G2 holonomy. These spaces are of interest for both theoretical and phenomenological reasons [2, 3, 4, 5, 6]. For orbifold backgrounds, and their partial resolutions, there are well known procedures for determining the gauge theory living on the probe worldvolume [7, 8]. (See [9] for examples of G2 holonomy orbifolds). However, recent attention has focused on asymptotically conical G2 manifolds for which the orbifold prescription is not relevant. Here we suggest a different approach to understand aspects of the probe theory, using mirror symmetry of three dimensional gauge theories [10]. Recall that mirror symmetry is a duality between a pair of three-dimensional field theories which, among other things, interchanges the Coulomb and Higgs branches. The basic observation is that mirror symmetry on an M2-brane probe has a simple interpretation as an “M-theory flip” [11]: