The Gravity dual of the Non-Perturbative $ N = 2 $ SUSY Yang-Mills Theory

TL;DR

This paper derives the anomalous Ward identity for N=2 SUSY Yang-Mills theories from wrapped D5 branes, leading to the Witten-Dijkgraaf-Verlinde-Verlinde equation and providing a non-perturbative solution avoiding the enhancon problem.

Contribution

It introduces a novel derivation of the Ward identity from wrapped branes, enabling non-perturbative analysis of N=2 SUSY Yang-Mills theories via holographic duality.

Findings

Derivation of the anomalous Ward identity from wrapped D5 branes.

Solution of the pre-potential using the Witten-Dijkgraaf-Verlinde-Verlinde equation.

Avoidance of the enhancon problem in non-perturbative regime.

Abstract

The anomalous Ward identity is derived for $N = 2$ SUSY Yang-Mills theories, which is resulted out of Wrapping of $D_5$ branes on Supersymmetric two cycles. From the Ward identity One obtains the Witten-Dijkgraaf-Verlinde-Verlinde equation and hence can solve for the pre-potential. This way one avoids the problem of enhancon which maligns the non-perturbative behaviour of the Yang-Mills theory resulted out of Wrapped branes.