Probing the dynamics of stringy flux tubes with large $R$-charge

TL;DR

This paper investigates the behavior of stringy flux tubes with large R-charge at strong coupling, revealing a non-analytic transition in the cusp anomalous dimension and analyzing fluctuations around classical solutions.

Contribution

It provides a unified description of the generalized cusp anomalous dimension for any cusp angle and R-charge, including the transition between Coulomb-like and deconfined regimes.

Findings

Identifies a critical R-charge where the behavior of the cusp anomaly changes non-analytically.

Derives fluctuation equations around the classical string solution for large R-charge.

Suggests implications for Wilson line fusion and field theory interpretations.

Abstract

We study the generalized cusp anomalous dimension, or quark-antiquark potential on the three-sphere, in the presence of a large $R$-charge $L$ and at strong coupling. Considering the insertion of a local scalar operator of charge $L$ on a cusped Wilson loop, we investigate the general solution of the dual string configuration for any value of cusp angles, paying particular attention to the different ranges of the physical parameters and obtaining a unified description that simultaneously captures the near BPS, the antiparallel lines and the large-$L$ regimes. We observe, in the limit of small separation between the lines, a non-analytic change in the behavior of the cusp anomaly at a critical value of $L$: one crosses from a region dominated by the familiar Coulomb-like singularity to a ``deconfined" situation describing the leading L\"uscher corrections at large $L$ of the generalized cusp anomalous dimension. We derive the equations for small fluctuations around the classical string solution, generalizing previous analysis of the uncharged case, and we study the behavior of the spectrum near the transition region. Finally, we speculate on the field theory origin of the transition and on its implications for the fusion of Wilson lines.