Branes Screening Quarks and Defect Operators

TL;DR

This paper uncovers a phase transition in AdS/BCFT where Wilson lines and surfaces exhibit a shift from Coulomb to perimeter law behavior, controlled by the brane angle, with implications for quark and defect operator interactions.

Contribution

It generalizes the computation of Wilson line potentials to Wilson surfaces in BCFTs with branes, revealing a phase transition controlled by the brane angle and extending the analysis to finite temperature.

Findings

Identifies a critical brane angle $ heta_{c,p}$ for Coulomb law scaling.

Shows the potential vanishes when the connecting surface ceases to exist.

Introduces a new regularization method at finite temperature.

Abstract

Here we generalize a well-known computation and uncover a phase-transition, showing that Wilson lines do not necessarily exhibit Coulomb scaling laws in AdS/BCFT at zero temperature. The area difference between a surface that returns to the boundary, and one that plunges into the bulk, determines the potential between two quarks. This classic AdS/CFT calculation is naturally extended to Wilson surfaces associated to general p-form symmetries in boundary conformal field theories (BCFTs) by embedding a Karch-Randall (KR) brane in the geometry. We find (generalized) Coulomb law scaling in subregion size $\Gamma$ is recovered only above the critical angle for the brane, $\theta_{c,p}$. The potential between the two quarks (or defect operators) vanishes precisely when the surface connecting them ceases to exist at $\theta_{c,p}$. This screening effect, where the operators are fully screened below the critical angle, is a phase transition from Coulomb law to perimeter law with the brane angle $\theta_b$ acting as an order parameter. This effect is also explored at finite temperature where we introduce a new regularization procedure to obtain closed-form results.