Spectral curves, emergent geometry, and bubbling solutions for Wilson loops

TL;DR

This paper explores the connection between spectral curves, emergent geometry, and bubbling solutions in the context of supersymmetric Wilson loops in N=4 super Yang-Mills theory, revealing how eigenvalue distributions encode dual geometries.

Contribution

It establishes that spectral curves from the matrix model correspond exactly to hyperelliptic surfaces describing bubbling supergravity solutions for Wilson loops.

Findings

Spectral curves are hyperelliptic surfaces.

Bubbling solutions are characterized by these spectral curves.

Wilson loop expectation values are analyzed via matrix model and supergravity.

Abstract

We study the supersymmetric circular Wilson loops of N=4 super Yang-Mills in large representations of the gauge group. In particular, we obtain the spectral curves of the matrix model which captures the expectation value of the loops. These spectral curves are then proven to be precisely the hyperelliptic surfaces that characterize the bubbling solutions dual to the Wilson loops, thus yielding an example of a geometry emerging from an eigenvalue distribution. We finally discuss the Wilson loop expectation value from the matrix model and from supergravity.