An Operator Product Expansion for Form Factors II. Born level

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 [ 1 ]. 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.