On a new type of divergence for spiky Wilson loops and related entanglement entropies

TL;DR

This paper investigates a novel divergence in Wilson loops with a specific spike configuration, revealing unique divergence behaviors at weak and strong coupling, with implications for entanglement entropy in lower-dimensional conformal field theories.

Contribution

It introduces a new divergence type for Wilson loops with a zero-angle cusp and curvature discontinuity, analyzing both weak and strong coupling cases, and connects findings to holographic entanglement entropy.

Findings

Leading divergence proportional to inverse square root of cutoff times curvature jump

Logarithmic divergence appears in supersymmetric case, absent in QCD

Strong coupling results from holography applicable to (2+1)-D CFT entanglement entropy

Abstract

We study the divergences of Wilson loops for a contour with a cusp of zero opening angle, combined with a nonzero discontinuity of its curvature. The analysis is performed in lowest order, both for weak and strong coupling. Such a spike contributes a leading divergent term proportional to the inverse of the square root of the cutoff times the jump of the curvature. As nextleading term appears a logarithmic one in the supersymmetric case, but it is absent in QCD. The strong coupling result, obtained from minimal surfaces in AdS via holography, can be used also for applications to entanglement entropy in (2+1)-dimensional CFT's.