Resummed tree heptagon

TL;DR

This paper advances the pentagon operator product expansion framework for planar N=4 SYM by successfully resumming the seven-leg tree NMHV amplitude, providing an exact space-time S-matrix at a given perturbation order.

Contribution

It extends the resummation techniques from hexagons to heptagons, enabling exact calculations of seven-leg NMHV amplitudes in planar N=4 SYM.

Findings

Resummed the seven-leg tree NMHV amplitude.

Constructed flux-tube integrands for all Grassmann components.

Achieved exact S-matrix in kinematical variables at a given perturbation order.

Abstract

The form factor program for the regularized space-time S-matrix in planar maximally supersymmetric gauge theory, known as the pentagon operator product expansion, is formulated in terms of flux-tube excitations propagating on a dual two-dimensional world-sheet, whose dynamics is known exactly as a function of 't Hooft coupling. Both MHV and non-MHV amplitudes are described in a uniform, systematic fashion within this framework, with the difference between the two encoded in coupling-dependent helicity form factors expressed via Zhukowski variables. The nontrivial SU(4) tensor structure of flux-tube transitions is coupling independent and is known for any number of charged excitations from solutions of a system of Watson and Mirror equations. This description allows one to resum the infinite series of form factors and recover the space-time S-matrix exactly in kinematical variables at a given order of perturbation series. Recently, this was done for the hexagon. Presently, we successfully perform resummation for the seven-leg tree NMHV amplitude. To this end, we construct the flux-tube integrands of the fifteen independent Grassmann component of the heptagon with an infinite number of small fermion-antifermion pairs accounted for in NMHV two-channel conformal blocks.