Wavy Wilson Line and AdS/CFT

TL;DR

The paper analyzes small deviations of Wilson lines (wavy lines) in ${\rm N}=4$ SYM under AdS/CFT, deriving a universal quadratic functional in the waviness that holds at both weak and strong coupling. Using perturbation theory and AdS minimal-surface methods, it shows the same functional form with a coupling-dependent coefficient that interpolates between linear in the weak-coupling limit and $\sqrt{g^2N}$ at strong coupling, with logarithmic structures carefully controlled. Supersymmetry is employed to simplify correlator computations and to prove that the straight line obeys the Migdal-Makeenko loop equation, while the wavy deformation preserves a related loop-equation structure. The results support a universal description of waviness in Wilson loops and illuminate UV/IR aspects and genus-resolved contributions to line-line correlators.

Abstract

Wilson loops which are small deviations from straight, infinite lines, called wavy lines, are considered in the context of the AdS/CFT correspondence. A single wavy line and the connected correlation function of a straight and wavy line are considered. It is argued that, to leading order in ``waviness'', the functional form of the loop is universal and the coefficient, which is a function of the 't Hooft coupling, is found in weak coupling perturbation theory and the strong coupling limit using the AdS/CFT correspondence. Supersymmetric arguments are used to simplify the computation and to show that the straight line obeys the Migdal-Makeenko loop equation.