Landau singularities of the 7-point ziggurat. Part I

Abstract

We compute the leading (first-type Landau) singularities of a certain four-loop 7-point graph that is related to the 7-point “ziggurat” graph by the graphical moves familiar from equivalent circuit theory. We find perfect agreement with a subset of the “heptagon symbol alphabet” that has appeared in the context of planar N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 super-Yang-Mills theory. The remaining heptagon symbol letters are found in its subleading Landau singularities, which we address in a companion paper.