Hexagon remainder function in the limit of self-crossing up to three loops

TL;DR

This paper investigates the behavior of the hexagon remainder function in planar N=4 SYM theory when the Wilson loop edges cross, providing higher-loop results and confirming previous divergence calculations.

Contribution

It extends the analysis of the hexagon remainder function to three loops in the crossing limit, offering new coefficients and confirming divergence structures.

Findings

Leading and next-leading divergences match previous results at two loops.

Derived coefficients for three-loop remainder function in crossing limit.

Confirmed analytic continuation of the remainder function.

Abstract

We consider Wilson loops in planar N=4 SYM for null polygons in the limit of two crossing edges. The analysis is based on a renormalisation group technique. We show that the previously obtained result for the leading and next-leading divergent term of the two loop hexagon remainder is in full agreement with the appropriate continuation of the exact analytic formula for this quantity. Furthermore, we determine the coefficients of the leading and next-leading singularity for the three loop remainder function for null n-gons with n >= 6.