Moduli Space Metric of N=2 Supersymmetric SU(N) Gauge Theory and the Enhancon

Abstract

We compute the moduli space metric of SU(N) Yang-Mills theory with N=2 supersymmetry in the vicinity of the point where the classical moduli vanish. This gauge theory may be realized as a set of N D7-branes wrapping a K3 surface, near the enhancon locus. The moduli space metric determines the low-energy worldvolume dynamics of the D7 branes near this point, including stringy corrections. Non-abelian gauge symmetry is not restored on the worldvolume at the enhancon point, but rather the gauge group remains U(1)^{N-1} and light electric and magnetically charged particles coexist. We also study the moduli space metric for a single probe brane in the background of N-1 branes near the enhancon point. We find quantum corrections to the supergravity probe metric that are not suppressed at large separations, but are down by 1/N factors, due to the response of the N-1 enhancon branes to the probe. A singularity appears before the probe reaches the enhancon point where a dyon becomes massless. We compute the masses of W-bosons and monopoles in a large N limit near this critical point.