Wilson loops: From four-dimensional SYM to two-dimensional YM

TL;DR

This paper shows that certain supersymmetric Wilson loops in N=4 super Yang-Mills theory on an S^2 are equivalent to observables in two-dimensional Yang-Mills theory, indicating a deep connection between the theories.

Contribution

It provides evidence that supersymmetric Wilson loops in N=4 SYM restricted to S^2 match two-dimensional YM observables, revealing a new link between four- and two-dimensional gauge theories.

Findings

Wilson loops in N=4 SYM on S^2 match 2D YM observables

The equivalence holds perturbatively and via AdS dual

Subsector of N=4 SYM is invariant under area-preserving diffeomorphisms

Abstract

In this note we study supersymmetric Wilson loops restricted to an S^2 submanifold of four-dimensional space in N=4 super Yang-Mills. We provide evidence from both perturbation theory and the AdS dual that those loops are equal to the analogous observables in two-dimensional Yang-Mills on S^2 (excluding non-perturbative contributions). This relates a subsector of N=4 SYM to a low-dimensional soluble model and also suggests that this subsector of N =4 SYM is invariant under area preserving diffeomorphisms.