Wilson loops correlators in defect $\mathcal{N}=4$ SYM

TL;DR

This paper studies the behavior of Wilson loop correlators in a defect version of $ ext{N}=4$ SYM at strong coupling, revealing complex phase transition patterns influenced by the defect.

Contribution

It introduces a detailed analysis of minimal surface saddle-points and phase transitions in defect $ ext{N}=4$ SYM, extending the understanding beyond the standard Gross-Ooguri transition.

Findings

Multiple saddle-point contributions due to the defect.

Complex phase transition patterns between minimal surfaces.

Dependence of transitions on spatial and internal parameters.

Abstract

We consider the correlator of two concentric circular Wilson loops with equal radii for arbitrary spatial and internal separation at strong coupling within a defect version of $\mathcal{N}=4$ SYM. Compared to the standard Gross-Ooguri phase transition between connected and disconnected minimal surfaces, a more complicated pattern of saddle-points contributes to the two-circles correlator due to the defect's presence. We analyze the transitions between different kinds of minimal surfaces and their dependence on the setting's numerous parameters.