Analytic Solution of Bremsstrahlung TBA II: Turning on the Sphere Angle

TL;DR

This paper provides an exact analytical solution to the Y-system for a cusped Wilson line in N=4 SYM, valid for any coupling and R-charge, unifying weak and strong coupling results and extending previous work.

Contribution

The authors derive a general analytical solution for the Y-system describing cusped Wilson lines, including sphere angle effects, and connect it with localization, classical string theory, and the FiNLIE framework.

Findings

Reproduces localization predictions at L=0

Matches classical string theory in the classical limit

Interpolates between weak and strong coupling regimes

Abstract

We find an exact analytical solution of the Y-system describing a cusped Wilson line in the planar limit of N=4 SYM. Our explicit solution describes anomalous dimensions of this family of observables for any value of the `t Hooft coupling and arbitrary R-charge L of the local operator inserted on the cusp in a near-BPS limit. Our finding generalizes the previous results of one of the authors & Sever and passes several nontrivial tests. First, for a particular case L=0 we reproduce the predictions of localization techniques. Second, we show that in the classical limit our result perfectly reproduces the existing prediction from classical string theory. In addition, we made a comparison with all existing weak coupling results and we found that our result interpolates smoothly between these two very different regimes of AdS/CFT. As a byproduct we found a generalization of the essential parts of the FiNLIE construction for the gamma-deformed case and discuss our results in the framework of the novel ${\bf P}\mu$-formulation of the spectral problem.