On the Holography of Free Yang-Mills

TL;DR

This paper explores the holographic duality between free Yang-Mills theory and a higher-dimensional gravity theory, analyzing spectrum, correlation functions, and one-loop partition functions to understand bulk-boundary correspondence.

Contribution

It provides new insights into the AdS/CFT duality for free Yang-Mills, including a shift in the bulk coupling constant and detailed spectral analysis.

Findings

Bulk coupling constant shifts to N^2 from N^2-1

Spectrum and correlation functions match boundary theory features

One-loop partition function supports the duality

Abstract

We study the AdS$_5$/CFT$_4$ duality where the boundary CFT is free Yang-Mills theory with gauge group SU(N). At the planar level we use the spectrum and correlation functions of the boundary theory to explicate features of the bulk theory. Further, by computing the one-loop partition function of the bulk theory using the methods of arXiv:1603.05387, we argue that the bulk coupling constant should be shifted to $N^2$ from $N^2-1$. Similar conclusions are reached by studying the dualities in thermal AdS$_5$ with $S^1\times S^3$ boundary.