An Operator Product Expansion for Form Factors

TL;DR

This paper introduces an operator product expansion framework for planar form factors in $ ext{N}=4$ SYM, utilizing dual conformal symmetry, and develops a bootstrap approach to determine a universal transition object, validated at one- and two-loop levels.

Contribution

It proposes a novel OPE for form factors based on dual conformal symmetry and introduces the 'form factor transition' with bootstrap constraints, advancing the understanding of form factors in $ ext{N}=4$ SYM.

Findings

Derived the form factor transition at leading order in perturbation theory.

Produced all-loop OPE predictions for MHV form factors.

Validated predictions by matching with existing one- and two-loop data.

Abstract

We propose an operator product expansion for planar form factors of local operators in $\mathcal{N}=4$ SYM theory. This expansion is based on the dual conformal symmetry of these objects or, equivalently, the conformal symmetry of their dual description in terms of periodic Wilson loops. A form factor is decomposed into a sequence of known pentagon transitions and a new universal object that we call the "form factor transition". This transition is subject to a set of non-trivial bootstrap constraints, which we expect to be sufficient to fully determine it. We evaluate the form factor transition for MHV form factors of the chiral half of the stress tensor supermultiplet at leading order in perturbation theory and use it to produce OPE predictions at any loop order. We match the one-loop and two-loop predictions with data available in the literature.