Gauge theories from wrapped and fractional branes

TL;DR

This paper compares two gauge/gravity dualities involving wrapped and fractional branes, deriving the running coupling and moduli space metric for a non-conformal N=4 super Yang-Mills theory in 2+1 dimensions.

Contribution

It provides a unified analysis of two different brane configurations and derives a general expression for the running coupling in terms of the stringy volume of the cycle.

Findings

Recovered the exact perturbative running coupling constant.

Derived the metric on the gauge theory's moduli space.

Established a general formula for the running coupling via stringy volume.

Abstract

We compare two applications of the gauge/gravity correspondence to a non conformal gauge theory, based respectively on the study of D-branes wrapped on supersymmetric cycles and of fractional D-branes on orbifolds. We study two brane systems whose geometry is dual to N=4, D=2+1 super Yang-Mills theory, the first one describing D4-branes wrapped on a two-sphere inside a Calabi-Yau two-fold and the second one corresponding to a system of fractional D2/D6-branes on the orbifold R^4/Z_2. By probing both geometries we recover the exact perturbative running coupling constant and metric on the moduli space of the gauge theory. We also find a general expression for the running coupling constant of the gauge theory in terms of the "stringy volume" of the two-cycle which is involved in both types of brane systems.