N=2 Gauge Theories from Wrapped Five-branes

TL;DR

The paper constructs string duals of four-dimensional N=2 pure SU(N) gauge theory by engineering D5-branes wrapped on two-cycles and uplifting seven-dimensional gauged supergravity solutions to ten dimensions. It identifies multiple points on the N=2 Coulomb branch, including a rotationally symmetric vev distribution and a linear distribution of vevs, using D5-probe analysis to recover the expected one-loop coupling structure and moduli-space geometry. The ten-dimensional uplift yields explicit metrics, dilatons, and fluxes, with UV behavior matching a linear-dilaton background and IR singularities controlled by an integration constant linked to the vev distribution. The second, more general solution with extra scalars reveals a holomorphic coupling tau that encodes a linearly distributed vev density mu(a), highlighting enhançon-like phenomena and deepening the holographic understanding of N=2 moduli spaces.

Abstract

We present string duals of four dimensional N=2 pure SU(N) SYM theory. The theory is obtained as the low energy limit of D5-branes wrapped on non-trivial two-cycles. Using seven dimensional gauged supergravity and uplifting the result to ten dimensions, we obtain solutions corresponding to various points of the N=2 moduli space. The more symmetric solution may correspond to a point with rotationally invariant classical vevs. By turning on seven dimensional scalar fields, we find a solution corresponding to a linear distribution of vevs. Both solutions are conveniently studied with a D5-probe, which also confirms many of the standard expectations for N=2 solutions.