An Operator Product Expansion for Form Factors II. Born level

TL;DR

This paper develops a non-perturbative operator product expansion for form factors in planar N=4 Super-Yang-Mills theory, computing leading two-particle transitions at Born level and testing the expansion against known data.

Contribution

It introduces explicit two-particle form factor transitions for the stress-tensor supermultiplet at Born level, advancing the non-perturbative OPE framework.

Findings

Computed two-particle form factor transitions at Born level.

Constructed Gubser-Klebanov-Polyakov two-particle singlet states.

Validated the OPE with perturbative data and made higher-loop predictions.

Abstract

Form factors in planar N=4 Super-Yang-Mills theory admit a type of non-perturbative operator product expansion (OPE), as we have recently shown in arXiv:2009.11297. This expansion is based on a decomposition of the dual periodic Wilson loop into elementary building blocks: the known pentagon transitions and a new object that we call form factor transition, which encodes the information about the local operator. In this paper, we compute the two-particle form factor transitions for the chiral part of the stress-tensor supermultiplet at Born level; they yield the leading contribution to the OPE. To achieve this, we explicitly construct the Gubser-Klebanov-Polyakov two-particle singlet states. The resulting transitions are then used to test the OPE against known perturbative data and to make higher-loop predictions.