A note on the dual of N=1 super Yang-Mills theory

TL;DR

This work refines the gauge/gravity dictionary for the Maldacena–Nuñez dual of $\mathcal{N}=1$ SYM by identifying the correct $S^2$ cycle in the ten-dimensional background, resolving a puzzle about the NSVZ $\beta$-function without resorting to singular coupling redefinitions. By carefully analyzing the ten-dimensional MN geometry and the role of seven-dimensional $SU(2)$ gauge transformations, the authors reproduce the $NSVZ$ $\beta$-function in the appropriate scheme and confirm the expected chiral anomalies and gaugino-related observables. The refined framework preserves the known non-perturbative features while showing that the MN construction naturally implements a geometric transition from a resolved to a deformed Calabi–Yau, in alignment with Vafa's proposal. The work thus strengthens holographic descriptions of confining $\mathcal{N}=1$ theories and clarifies cycle-identification issues essential for reliable gauge/gravity correspondence calculations.

Abstract

We refine the dictionary of the gauge/gravity correspondence realizing N=1 super Yang-Mills by means of D5-branes wrapped on a resolved Calabi-Yau space. This is done by fixing an ambiguity on the correct interpretation of the holographic dual of the running gauge coupling and amounts to identify a specific 2-cycle in the dual ten-dimensional supergravity background. In doing so, we also discuss the role played in this context by gauge transformations in the relevant seven-dimensional gauged supergravity. While all nice properties of the duality are maintained, this modification of the dictionary has some interesting physical consequences and solves a puzzle recently raised in the literature. In this refined framework, it is also straightforward to see how the correspondence naturally realizes a geometric transition.