Fermionic pentagons and NMHV hexagon

TL;DR

This paper investigates the structure of NMHV hexagon amplitudes in planar N=4 super Yang-Mills theory by analyzing fermionic pentagons within the operator product expansion framework, providing new insights into their form factors and bootstrap equations.

Contribution

It introduces the form factor couplings of fermionic pentagons in the OPE for NMHV amplitudes and confirms their bootstrap solutions across all couplings.

Findings

Derived form factor couplings for fermionic pentagons.

Validated bootstrap equations for nonsinglet pentagons.

Matched four-loop order super Wilson loop results.

Abstract

We analyze the near-collinear limit of the null polygonal hexagon super Wilson loop in the planar N = 4 superYang-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.