A Two-Loop Octagon Wilson Loop in N = 4 SYM

TL;DR

This paper analytically computes a two-loop eight-edged Wilson loop in planar N=4 SYM, revealing its remainder function's structure and testing universality conjectures by comparing weak and strong coupling results.

Contribution

It provides the first analytic two-loop computation of an octagon Wilson loop in N=4 SYM and explores the universality of the remainder function across coupling regimes.

Findings

Remainder function expressed with weight four transcendental functions

Comparison confirms universality conjecture of the remainder function

First analytic result for a two-loop octagon Wilson loop in this theory

Abstract

In the planar N = 4 supersymmetric Yang-Mills theory at weak coupling, we perform the first analytic computation of a two-loop eight-edged Wilson loop embedded into the boundary of AdS3. Its remainder function is given as a function of uniform transcendental weight four in terms of a constant plus a product of four logarithms. We compare to the strong-coupling result, and test a conjecture on the universality of the remainder function proposed in the literature.