Semiclassics at the cusp

TL;DR

This paper develops a semiclassical approach to analyze cusped Wilson line operators in the Abelian Higgs model at large charges, providing analytic results beyond fixed-order perturbation theory.

Contribution

It introduces a double-scaling limit framework that allows analytic control over large-charge regimes and computes the cusp anomalous dimension up to NNLO, resumming scalar interactions.

Findings

Computed cusp anomalous dimension for arbitrary charges up to NNLO.

Resummed scalar self-interactions to all orders.

Provided new predictions for defect CFT observables.

Abstract

We study cusped Wilson line operators in the Abelian Higgs model in $ d = 4 - \epsilon $ at large external charges. Using a double-scaling limit $ Q \to \infty $, $ \epsilon \to 0 $ with $ Q\epsilon $ fixed, we develop a semiclassical framework that provides analytic control beyond fixed-order perturbation theory. We compute the cusp anomalous dimension for arbitrary charges up to next-to-next-to-leading order in the gauge coupling, while resumming scalar self-interactions to all orders. Our results interpolate between perturbative and large-charge regimes, accessing domains that are invisible in fixed-order perturbation theory. As an application, we provide new predictions for various defect CFT observables, including the Mandelstam-Schwinger-dressed two-point function characterizing the superconducting phase transition.