Wilson Loop Correlator in the AdS/CFT Correspondence

TL;DR

This paper investigates the phase transition in Wilson loop correlators within the AdS/CFT framework, focusing on two circular loops and analyzing the effects of string fluctuations on the transition's nature.

Contribution

It provides a detailed analysis of the Wilson loop correlator phase transition in AdS/CFT, including the impact of string world sheet fluctuations at finite coupling.

Findings

Identified a phase transition in Wilson loop correlators at strong coupling.

Showed that string fluctuations smooth out the transition at finite coupling.

Discussed general implications for Wilson loop correlators in gauge theories.

Abstract

The AdS/CFT correspondence predicts a phase transition in Wilson loop correlators in the strong coupling N=4, D=4 SYM theory which arises due to instability of the classical string stretched between the loops. We study this transition in detail by solving equations of motion for the string in the particular case of two circular Wilson loops. The transition is argued to be smoothened at finite `t Hooft coupling by fluctuations of the string world sheet and to be promoted to a sharp crossover. Some general comments about Wilson loop correlators in gauge theories are made.