Wilson Loops in N=4 SYM and Fermion Droplets

TL;DR

This paper explores the matrix model representation of Wilson loops in N=4 SYM, revealing a fermion droplet picture, a selection rule for correlators, and phase transitions in large representations.

Contribution

It introduces a fermion droplet interpretation for Wilson loops and uncovers new selection rules and phase transition phenomena in large N limits.

Findings

Fermion droplet picture emerges in large N limit.

Selection rule: non-zero correlator only if chiral primary has a single hook.

Phase transition in expectation value for large Young diagram representations.

Abstract

The matrix models which are conjectured to compute the circle Wilson loop and its correlator with chiral primary operators are mapped onto normal matrix models. A fermion droplet picture analogous to the well-known one for chiral primary operators is shown to emerge in the large N limit. Several examples are computed. We find an interesting selection rule for the correlator of a single trace Wilson loop with a chiral primary operator. It can be non-zero only if the chiral primary is in a representation with a single hook. We show that the expectation value of the Wilson loop in a large representation labelled by a Young diagram with a single row has a first order phase transition between a regime where it is identical to a large column representation and a regime where it is a large wrapping number single trace Wilson loop.