Gauge theories from wrapped and fractional branes

Abstract We compare two applications of the gauge/gravity correspondence to a nonconformal 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.