Abstract
We propose an operator product expansion for planar form factors of local operators in 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 nontrivial bootstrap constraints, which are sufficient to fully determine it. We evaluate the form factor transition for maximally helicity-violating form factors of the chiral half of the stress tensor supermultiplet at leading order in perturbation theory and use it to produce operator product expansion predictions at any loop order. We match the one-loop and two-loop predictions with data available in the literature.
Highlights
Introduction.—The past ten years saw huge progress in our understanding of null polygonal Wilson loops, which was primarily motivated by the fact that these objects describe color-ordered scattering amplitudes in planar N 1⁄4 4 SYM theory
We propose an operator product expansion for planar form factors of local operators in N 1⁄4 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
Summary
We propose an operator product expansion for planar form factors of local operators in N 1⁄4 4 SYM theory. Introduction.—The past ten years saw huge progress in our understanding of null polygonal Wilson loops, which was primarily motivated by the fact that these objects describe color-ordered scattering amplitudes in planar N 1⁄4 4 SYM theory Another motivation lies in them controlling a certain limit of correlation functions of local operators in this theory [1,2,3,4,5]. The only systematic method of studying scattering amplitudes is the operator product expansion (OPE), which is based on dual conformal symmetry [14] This powerful property of planar amplitudes is nothing but the conformal symmetry of their dual description in terms of null polygonal Wilson loops.
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