Matrix pentagons

TL;DR

This paper completes the description of pentagon transitions in the Operator Product Expansion for null polygonal Wilson loops in planar N=4 SYM by solving the SU(4) matrix structure using recursive methods.

Contribution

It provides a recursive solution for the SU(4) matrix structure of singlet pentagons, completing the understanding of multiparticle pentagon transitions in the OPE framework.

Findings

Solved the SU(4) matrix structure for singlet pentagons.

Derived charged pentagons from singlet pentagons via a limiting procedure.

Provided a complete description of pentagon transitions as functions of the 't Hooft coupling.

Abstract

The Operator Product Expansion for null polygonal Wilson loop in planar maximally supersymmetric Yang-Mills theory runs systematically in terms of multiparticle pentagon transitions which encode the physics of excitations propagating on the color flux tube ending on the sides of the four-dimensional contour. Their dynamics was unravelled in the past several years and culminated in a complete description of pentagons as an exact function of the 't Hooft coupling. In this paper we provide a solution for the last building block in this program, the SU(4) matrix structure arising from internal symmetry indices of scalars and fermions. This is achieved by a recursive solution of the Mirror and Watson equations obeyed by the so-called singlet pentagons and fixing the form of the twisted component in their tensor decomposition. The non-singlet, or charged, pentagons are deduced from these by a limiting procedure.