Landau singularities of the 7-point ziggurat. Part II

Abstract

We solve the Landau equations to find the singularities of nine three-loop 7-point graphs that arise as relaxations of the graph studied in [22]. Along the way we establish that Y − ∆ equivalence fails for certain branches of solutions to the Landau equations. We find two graphs with singularities outside the heptagon symbol alphabet; in particular they are not cluster variables of Gr(4, 7). We compare maximal residues of scalar graphs exhibiting these singularities to those in $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory in order to probe their cancellation from its amplitudes.