Supersymmetric Wilson loops at two loops

TL;DR

This paper performs a two-loop quantum analysis of supersymmetric Wilson loops in N=4 SYM, confirming conjectured exact results from matrix models and indicating potential localization techniques.

Contribution

It provides the first complete two-loop computation of cusped Wilson loops on S^2, validating the matrix model conjecture and revealing intricate diagrammatic cancellations.

Findings

Two-loop results match matrix model predictions

Ladder diagrams and self-energy contributions interplay complexly

Supports the existence of a localization procedure for these loops

Abstract

We study the quantum properties of certain BPS Wilson loops in ${\cal N}=4$ supersymmetric Yang-Mills theory. They belong to a general family, introduced recently, in which the addition of particular scalar couplings endows generic loops on $S^3$ with a fraction of supersymmetry. When restricted to $S^2$, their quantum average has been further conjectured to be exactly computed by the matrix model governing the zero-instanton sector of YM$_2$ on the sphere. We perform a complete two-loop analysis on a class of cusped Wilson loops lying on a two-dimensional sphere, finding perfect agreement with the conjecture. The perturbative computation reproduces the matrix-model expectation through a highly non-trivial interplay between ladder diagrams and self-energies/vertex contributions, suggesting the existence of a localization procedure.