OPE for null Wilson loops and open spin chains

Abstract

Maximal helicity-violating scattering amplitudes in N=4 supersymmetric Yang-Mills theory are dual to Wilson loops on closed null polygons. We perform their operator product expansion analysis in two-dimensional kinematics in the soft-collinear approximation which corresponds to the case when some light-cone distances vanish. We construct the expansion in terms of multi-particle "heavy"-light operators, where the "heavy" fields are identified with the Wilson lines defining the OPE channel and the light fields emerge from the curvature of the contour. The correlation function of these define the remainder function. We study the dilatation operator for these operators at one loop order and find that it corresponds to a non-compact open spin chain. This provides an alternative view on elementary excitations propagating on the GKP string at weak coupling, which now correspond to particles traveling along an open spin chain. The factorized structure of the Wilson loop in the soft limit allows one to represent the two-loop correction to the octagon Wilson loop as a convolution formula and find the corresponding remainder function.

Figures (2)

• Figure 1: Null Wilson loop in the $R^{1,1}$ kinematics (left) and leading term contribution to its operator expansion in the soft-collinear limit $x_{23}^+, \, x_{67}^+ \to 0$.
• Figure 2: One-loop dilatation operator for the "heavy"-light operator $\Phi$.