Algebraic Curve for a Cusped Wilson Line

TL;DR

This paper derives a classical algebraic curve for a cusped Wilson line with R-charge in planar N=4 SYM, enabling calculation of the cusp anomalous dimension and its 1-loop correction in the classical limit.

Contribution

It introduces a matrix model reformulation and constructs a classical algebraic curve for the cusp anomalous dimension, extending previous quantum results to the classical regime.

Findings

Derived the classical algebraic curve for the cusped Wilson line

Computed the classical cusp anomalous dimension from the curve

Calculated the 1-loop correction and validated results numerically

Abstract

We consider the classical limit of the recently obtained exact result for the anomalous dimension of a cusped Wilson line with the insertion of an operator with L units of R-charge at the cusp in planar N=4 SYM. The classical limit requires taking both the 't Hooft coupling and L to infinity. Since the formula for the cusp anomalous dimension involves determinants of size proportional to L, the classical limit requires a matrix model reformulation of the result. We construct such matrix model-like representation and find corresponding classical algebraic curve. Using this we derive the classical value of the cusp anomalous dimension and the 1-loop correction to it. We check our results against the energy of the classical solution and numerically by extrapolating from the quantum regime of finite L.