Descent equation for superloop and cyclicity of OPE

TL;DR

This paper investigates the Descent Equation for supersymmetric Wilson loops within the pentagon OPE framework, addressing cyclicity issues and twist phenomena, and verifies the all-order relation between NMHV and MHV configurations through perturbative checks.

Contribution

It introduces a method to restore cyclicity in the Descent Equation and explores twist enhancement phenomena, providing a consistency check for the all-order relation between NMHV and MHV loops.

Findings

Verified the all-order Descent Equation in perturbation theory.

Discovered twist enhancement when shifting OPE channels.

Established a relation between different twist contributions.

Abstract

We study the so-called Descent, or Q-bar, Equation for the null polygonal supersymmetric Wilson loop in the framework of the pentagon operator product expansion. To properly address this problem, one requires to restore the cyclicity of the loop broken by the choice of OPE channels. In the course of the study, we unravel a phenomenon of twist enhancement when passing to a cyclically shifted channel. Currently, we focus on the consistency of the all-order Descent equation for the particular case relating the NMHV heptagon to MHV hexagon. We find that the equation establishes a relation between contributions of different twists and successfully verify it in perturbation theory making use of available bootstrap predictions for elementary pentagons.