N=1 and N=2 Super Yang-Mills theories from wrapped branes

TL;DR

The paper uses wrapped D5-branes on supersymmetric 2-cycles to realize four-dimensional SU(N) SYM theories with N=1 and N=2 supersymmetry via gauge/gravity duality. It derives the complete NSVZ beta-function for the N=1 theory from the Maldacena–Nuñez solution and uncovers non-perturbative fractional instanton corrections that smooth the running, alongside a gravity dual of the gaugino condensate and a chiral anomaly. For the N=2 case, it extracts the perturbative beta-function and chiral anomaly from a regular background, while IR non-perturbative effects are impeded by singularities in alternative solutions. The work establishes a concrete map between gravity coordinates and gauge-theory scales through protected operators, enabling quantitative insights into running couplings, anomalies, and instanton structures in both theories.

Abstract

We consider supergravity solutions of D5 branes wrapped on supersymmetric 2-cycles and use them to discuss relevant features of four-dimensional N=1 and N=2 super Yang-Mills theories with gauge group SU(n). In particular in the N=1 case, using a gravitational dual of the gaugino condensate, we obtain the complete NSVZ beta-function. We also find non-perturbative corrections associated to fractional instantons with charge 2/n. These non-perturbative effects modify the running of the coupling constant which remains finite even at small scales in a way that resembles to the soft confinement scenario of QCD.