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

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.

19 pages, 4 figures, typos corrected, comment on relation to recent results for the symbol of three-loop remainder added, version to appear in JHEP

References in corpus (6)

• Gluon scattering amplitudes at strong coupling
• Classical Polylogarithms for Amplitudes and Wilson Loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Hexagon Wilson loop = six-gluon MHV amplitude
• Bootstrapping the three-loop hexagon
• A Surprise in the Amplitude/Wilson Loop Duality

Cited by in corpus (4)

• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• All orders results for self-crossing Wilson loops mimicking double parton scattering
• The Cross Anomalous Dimension in Maximally Supersymmetric Yang--Mills Theory