Operator Product Expansion for Form Factors

Abstract

Form factors in planar N = 4 Super-Yang-Mills theory admit a type of nonperturbative 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.

A three-point form factor through five loops

“…6 6. Near-collinear limit: The near collinear limit of R should agree with the predictions of the FFOPE [60][61][62].…”

“…Their expansion around this limit is described at all loop orders by the integrability-based pentagon operator product expansion (POPE) [50][51][52][53][54][55][56][57][58][59]. Recently, an analogous description of the near-collinear limit of form factors has been developed, termed the form factor operator product expansion (FFOPE) [60][61][62]. It provides physical constraints on the near-collinear behavior of the form factors of the chiral part of the stress-tensor supermultiplet at any loop order.…”

“…An important source of data for the perturbative form factor bootstrap stems from the near-collinear limit. Using the recently developed form factor operator product expansion, or FFOPE, the form factor can be determined in an expansion around the collinear limit for any value of the planar coupling constant [60][61][62]. Let us briefly review this construction.…”

“…Note that dual conformal symmetry acts on both the dual momenta and the periodicity constraint. Using dual momentum space, the expectation value of the (suitably regularized) Wilson loop can be written in terms of dual conformal cross ratios [60]. For the three-point form factor, we have…”

Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality

“…Another important structure to explore is the color-kinematics duality, in particular for form factors of general non-BPS operators at two loops. Furthermore, the form factors at strong coupling via AdS/CFT have been studied in [4,5,12], and more recently, the Pentagon OPE method has been generalized to form factor [136]. It would be certainly interesting to have a non-planar generalization (see a related study for amplitudes [137]).…”