Quantum Spectral Curve for a Cusped Wilson Line in N=4 SYM

TL;DR

This paper extends the Quantum Spectral Curve formalism to compute the generalized cusp anomalous dimension in N=4 SYM, providing analytical and numerical results that match perturbative and string theory predictions.

Contribution

It introduces a modified QSC approach for the cusp anomalous dimension, including all-loop analytic expressions and nonperturbative numerical results.

Findings

All-loop analytic expression for small angle expansion.

Numerical results matching 4-loop perturbation theory.

Agreement with classical string predictions.

Abstract

We show that the Quantum Spectral Curve (QSC) formalism, initially formulated for the spectrum of anomalous dimensions of all local single trace operators in N=4 SYM, can be extended to the generalized cusp anomalous dimension for all values of the parameters. We find that the large spectral parameter asymptotics and some analyticity properties have to be modified, but the functional relations are unchanged. As a demonstration, we find an all-loop analytic expression for the first two nontrivial terms in the small |phi \pm theta| expansion. We also present nonperturbative numerical results at generic angles which match perfectly 4-loop perturbation theory and the classical string prediction. The reformulation of the problem in terms of the QSC opens the possibility to explore many open questions. We attach to this paper several Mathematica notebooks which should facilitate future studies.