Precision Holography for 5D Super Yang-Mills

TL;DR

This paper computes the vacuum expectation value of 1/2-BPS Wilson loops in 5D super Yang-Mills theory using holography, addressing quantum corrections and divergences to match gauge theory results.

Contribution

It provides a detailed holographic calculation of Wilson loop vevs in 5D MSYM, including next-to-leading order corrections and divergence handling, which was not previously achieved.

Findings

Holographic computation matches gauge theory Wilson loop vevs

Quantum corrections involve dilaton coupling and worldsheet fluctuations

Proper treatment of divergences yields finite, consistent results

Abstract

We study 1/2-BPS Wilson loop (WL) operators in maximally supersymmetric Yang-Mills theory (MSYM) on $\mathbf{S}^5$. Their vacuum expectation value (vev) can be computed exactly at large $N$ thanks to supersymmetric localization. The holographic dual to MSYM on $\mathbf{S}^5$ is geometrically realized by a stack of $N$ D4-branes with spherical worldvolume in ten dimensions. We compute the vev of the circular WL using holography by evaluating the partition function of a fundamental string in this background. Our focus is on the next-to-leading order correction to the string partition function which is composed of two parts; the dilaton coupling to the worldsheet and the one-loop fluctuations of the worldsheet itself. We face a variety of issues, some related to the presence of a non-constant dilaton, and others that are common to its AdS analogue. However, the universality of UV divergences as well as the importance of a proper choice of an IR regulator have been recently stressed in the literature. Inspired by this, we resolve our issues by first carefully treating the Weyl anomaly which receives contributions from the non-constant dilaton, and then by computing the ratio of our partition function and the one of a string in AdS$_4\times \mathbf{C}P^3$, which is dual to a 1/2-BPS WL in ABJM. Crucially, this approach yields a finite result which matches the corresponding ratio of WL vevs on the gauge theory side.