Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators

TL;DR

This paper introduces a dual Wilson loop description for super form factors of half-BPS operators in planar N=4 super-Yang-Mills, providing explicit weak coupling calculations and extending the OPE framework to these form factors.

Contribution

It proposes a novel duality between super form factors and Wilson loops, and extends the OPE approach to include higher-charge operators at any coupling.

Findings

Wilson loop matrix elements match known super form factors at one loop

Tree-level interactions localize at cusps, linking to the amplituhedron

Two-loop weak coupling checks confirm the conjectured OPE blocks

Abstract

We propose a dual Wilson loop description for the MHV super form factors of half-BPS operators in planar $\mathcal{N}=4$ super-Yang-Mills theory. In this description, the local operators are represented by on-shell states, made out of zero-momentum particles, that are absorbed by a null periodic super Wilson loop. We present evidence for this duality at weak coupling, by performing an explicit calculation of the Wilson loop matrix elements through one loop. At tree level, the interactions localize at the cusps of the loop, revealing a simple connection between the super form factors and the $m=2$ tree amplituhedron. At loop level, we show that the Wilson loop calculation reproduces the known results for the super form factors. Inspired by this duality, we extend the OPE program developed for the form factors of the Lagrangian to the super form factors of the higher-charge operators. We introduce non-perturbative axioms and conjectures for the main building blocks that govern the exchange of the lightest flux-tube excitations. These blocks appear as simple refinements of the form factor transitions introduced in earlier OPE studies. They are expressed at any value of the 't Hooft coupling in terms of the tilted Beisert-Eden-Staudacher kernel. We carry out checks of our conjectures up to two loops at weak coupling for three- and four-point form factors of half-BPS operators of various lengths, finding perfect agreement with perturbative data.