Multichannel Conformal Blocks for Polygon Wilson Loops

TL;DR

This paper introduces Multichannel Conformal Blocks for analyzing null polygon Wilson loops with more than six edges, enabling decomposition and prediction of multi-loop results in the OPE framework.

Contribution

It develops the concept of Multichannel Conformal Blocks for complex polygons and applies them to decompose and predict higher-loop Wilson loop results.

Findings

Decomposed one-loop heptagon Wilson loop

Predicted two-loop OPE discontinuities

Provided predictions for all-loop order results

Abstract

We introduce the notion of Multichannel Conformal Blocks relevant for the Operator Product Expansion for Null Polygon Wilson loops with more than six edges. As an application of these, we decompose the one loop heptagon Wilson loop and predict the value of its two loop OPE discontinuities. At the functional level, the OPE discontinuities are roughly half of the full result. Using symbols they suffice to predict the full two loop result. We also present several new predictions for the heptagon result at any loop order.