Landau Singularities of the 7-Point Ziggurat I

TL;DR

This paper calculates the leading Landau singularities of a specific four-loop 7-point graph, revealing connections to the heptagon symbol alphabet in planar N=4 super-Yang-Mills theory, and discusses subleading singularities.

Contribution

It provides the first computation of Landau singularities for a four-loop 7-point graph related to the heptagon alphabet, linking graph theory with quantum field theory.

Findings

Agreement with the heptagon symbol alphabet for leading singularities

Identification of subleading Landau singularities related to remaining symbol letters

Extension of Landau analysis to complex multi-loop, multi-point graphs

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 $\mathcal{N}=4$ super-Yang-Mills theory. The remaining heptagon symbol letters are found in its subleading Landau singularities, which we address in a companion paper.