Wilson Loops and Spherical Branes

TL;DR

This paper investigates the holographic computation of 1/2-BPS Wilson loops in supersymmetric Yang-Mills theories on spheres of various dimensions, focusing on next-to-leading order corrections and divergence structures in non-conformal cases.

Contribution

It develops a framework for calculating holographic Wilson loops beyond leading order in non-conformal backgrounds with non-constant dilaton fields.

Findings

Successfully matched sub-leading scaling with al and N.

Identified non-universal divergence structures in one-loop partition functions.

Provided a method to handle divergences and approach numerical prefactor calculation.

Abstract

We study 1/2-BPS Wilson loop operators in maximally supersymmetric Yang-Mills theory on $d$-dimensional spheres. Their vacuum expectation values can be computed at large $N$ through supersymmetric localisation. The holographic duals are given by back-reacted spherical D-branes. For $d\neq 4$, the resulting theories are non-conformal and correspondingly, the dual geometries do not possess an asymptotic AdS region. The main aim of this work is to compute the holographic Wilson loops by evaluating the partition function of a probe fundamental string and M2-brane in the dual geometry, focusing on the next-to-leading order. Along the way, we highlight a variety of issues related to the presence of a non-constant dilaton. In particular, the structure of the divergences of the one-loop partition functions takes a non-universal form in contrast to examples available in the literature. We devise a general framework to treat the divergences, successfully match the sub-leading scaling with $\lambda$ and $N$, and provide a first step towards obtaining the numerical prefactor.