Phase transitions in Wilson loop correlator from integrability in global AdS

TL;DR

This paper computes Wilson loop correlators in AdS/CFT using integrability and minimal surfaces, revealing phase transition behavior influenced by the size of the boundary sphere.

Contribution

It introduces a method to analyze Wilson loop correlators in global AdS by leveraging integrability and minimal surface solutions, highlighting the impact of sphere size on phase transitions.

Findings

Connected solutions dominate for small loops, disconnected for large loops.

No transition occurs for sufficiently large Wilson loops due to sphere size constraints.

The approach employs integrability to explicitly construct minimal surfaces.

Abstract

We directly compute Wilson loop/Wilson loop correlators on ${\mathbb R}\times $S$^3$ in AdS/CFT by constructing space-like minimal surfaces that connect two space-like circular contours on the boundary of global AdS that are separated by a space-like interval. We compare these minimal surfaces to the disconnected "double cap" solutions both to regulate the area, and show when the connected/disconnected solution is preferred. We find that for sufficiently large Wilson loops no transition occurs because the Wilson loops cannot be sufficiently separated on the sphere. This may be considered an effect similar to the Hawking-Page transition: the size of the sphere introduces a new scale into the problem, and so one can expect phase transitions to depend on this data. To construct the minimal area solutions, we employ a reduction a la Arutyunov-Russo-Tseytlin (used by them for spinning strings), and rely on the integrability of the reduced set of equations to write explicit results.