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

TL;DR

This paper uses supergravity solutions of wrapped D5 branes to explore four-dimensional N=1 and N=2 super Yang-Mills theories, deriving the NSVZ beta-function and identifying non-perturbative effects like fractional instantons.

Contribution

It provides a gravitational dual approach to derive the NSVZ beta-function and uncovers non-perturbative corrections in super Yang-Mills theories.

Findings

Derived the complete NSVZ beta-function from supergravity solutions.

Identified non-perturbative effects from fractional instantons with charge 2/n.

Showed the coupling remains finite at small scales, resembling QCD confinement.

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.