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

TL;DR

This paper refines the gauge/gravity duality for N=1 super Yang-Mills by clarifying the holographic dual of the gauge coupling, leading to better understanding of the dual geometry and resolving recent puzzles.

Contribution

It provides a refined dictionary for the gauge/gravity correspondence involving D5-branes on a resolved Calabi-Yau, clarifying the dual of the running gauge coupling.

Findings

Identifies a specific 2-cycle in the supergravity background.

Maintains the properties of the duality while resolving a recent puzzle.

Shows how the duality naturally realizes a geometric transition.

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.