Abstract
We analyze the near-collinear limit of the null polygonal hexagon super Wilson loop in the planar N=4 super-Yang–Mills theory. We focus on its Grassmann components which are dual to next-to-maximal helicity-violating (NMHV) scattering amplitudes. The kinematics in question is studied within a framework of the operator product expansion that encodes propagation of excitations on the background of the color flux tube stretched between the sides of Wilson loop contour. While their dispersion relation is known to all orders in 't Hooft coupling from previous studies, we find their form factor couplings to the Wilson loop. This is done making use of a particular tessellation of the loop where pentagon transitions play a fundamental role. Being interested in NMHV amplitudes, the corresponding building blocks carry a nontrivial charge under the SU(4) R-symmetry group. Restricting the current consideration to twist-two accuracy, we analyze two-particle contributions with a fermion as one of the constituents in the pair. We demonstrate that these nonsinglet pentagons obey bootstrap equations that possess consistent solutions for any value of the coupling constant. To confirm the correctness of these predictions, we calculate their contribution to the super Wilson loop demonstrating agreement with recent results to four-loop order in 't Hooft coupling.
Highlights
In recent years, the planar maximally supersymmetric gauge theory took on the status of a proverbial “harmonic oscillator” of field theories, i.e., a solvable dynamical model of gauge interactions in four dimensions
Having discussed the S-matrices, let us turn to the axioms for the pentagon transitions that are defined by the following matrix elements
Within the framework of the pentagon operator product expansion introduced in Ref. [12], we discussed twist-two contributions to the hexagon next-to-maximal helicity-violating (NMHV) amplitude, elaborating and generalizing our previous consideration [16]
Summary
The planar maximally supersymmetric gauge theory took on the status of a proverbial “harmonic oscillator” of field theories, i.e., a solvable dynamical model of gauge interactions in four dimensions. The fundamental excitations of the flux tube consist of the hole, fermions and gluons (as well as bound states of the latter) Their energies and momenta are known nonperturbatively [13]. To successfully determine the near-collinear expansion of the Wilson loop, one has to determine the coupling of the flux-tube excitations to the perimeter links These are encoded in the so-called pentagon form factors [12]. In our previous analysis [16], this formalism was extended to account for contributions with non-trivial representations with respect to SU(4), focusing on a specific NMHV channel that transforms in the 6 of the R-symmetry group We conclude this discussion by proposing nonperturbative formulas for other two-particle states. We provide a summary of scattering matrices and their mirrors for all pentagon transitions discussed in the main body of the paper
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