OPE for null Wilson loops and open spin chains

TL;DR

This paper analyzes null Wilson loops in N=4 SYM using OPE in two-dimensional kinematics, revealing a connection to open spin chains and providing a new perspective on excitations in the theory.

Contribution

It introduces an OPE framework for null Wilson loops that maps the problem to open spin chains, offering a novel weak-coupling interpretation of excitations.

Findings

Dilatation operator corresponds to a non-compact open spin chain.

Two-loop correction to the octagon Wilson loop expressed as a convolution.

Reveals a new weak-coupling picture of elementary excitations.

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.