Phase transition in Wilson loop correlator from AdS/CFT correspondence

TL;DR

This paper extends the analysis of phase transitions in Wilson loop correlators within AdS/CFT to concentric circles of unequal radii, revealing new instability features and minimal surface behaviors.

Contribution

It introduces a generalized calculation of Wilson loop phase transitions for unequal radii and analyzes the stability and minimal surface configurations in this scenario.

Findings

Phase transition occurs due to classical string instability.

Connected minimal surface is subleading or absent when radii differ significantly.

New features are identified that have no flat space analogue.

Abstract

A previous calculation of the phase transition in the Wilson loop correlator in the zero temperature AdS/CFT correspondence is extended to the case where the loops are concentric circles of unequal radii. This phase transition occurs due to the instability of the classical string stretched between the loops. We compute the string action and its expansion in the distance h between the loops for small h. We also find that the connected minimal surface is subleading or does not even exist when h=0 and the radii are considerably different. This feature has no analogue in flat space.