A Rosetta Stone for Wilson Line Defects

TL;DR

This paper constructs a detailed map linking weak and strong coupling regimes for Wilson line defects in N=4 Super-Yang-Mills, predicting state dimension doubling and validating it through integrability-based spectrum analysis.

Contribution

It introduces a novel mapping between gauge and string degrees of freedom for Wilson line defects, extending the Quantum Spectral Curve to charged sectors and testing predictions with integrability.

Findings

State dimensions double from zero to infinite coupling.

Validated the mapping using integrability-based spectrum results.

Extended Quantum Spectral Curve to charged sectors.

Abstract

In this paper, we discuss the construction of a map between weak (gauge) and strong (string) coupling degrees of freedom for the supersymmetric Wilson line-defect in the planar N=4 Super-Yang-Mills. By analysing the Partition Functions at zero and infinite coupling, we propose a map from degrees of freedom capturing single- and singlet two-particle states at zero coupling to infinite coupling. This map predicts that the dimension of states in these particular sectors doubles as it goes from zero to infinite coupling. We test this prediction against the non-perturbative spectrum of insertions on the Wilson line obtained using integrability. In addition to already available integrability-based results, we obtain the non-perturbative scaling dimensions of the simplest non-trivial operators with transverse spin about the Wilson line, thereby extending the Quantum Spectral Curve construction to such charged sectors.