Landau Singularities and Symbology: One- and Two-loop MHV Amplitudes in SYM Theory

TL;DR

This paper investigates the Landau singularities of one- and two-loop MHV amplitudes in planar N=4 super-Yang-Mills theory, revealing that all two-loop symbol entries are linked to one-loop Landau singularities.

Contribution

It applies Landau equations to identify branch points in Feynman integrals and connects these singularities to the symbol entries of MHV amplitudes, highlighting their relation across loop orders.

Findings

All two-loop MHV amplitude symbol entries are present as Landau singularities of one-loop pentagon integrals.

Landau equations effectively characterize the branch points relevant to amplitude symbols.

The study clarifies the structure of singularities in planar N=4 SYM amplitudes.

Abstract

We apply the Landau equations, whose solutions parameterize the locus of possible branch points, to the one- and two-loop Feynman integrals relevant to MHV amplitudes in planar $\mathcal{N}=4$ super-Yang-Mills theory. We then identify which of the Landau singularities appear in the symbols of the amplitudes, and which do not. We observe that all of the symbol entries in the two-loop MHV amplitudes are already present as Landau singularities of one-loop pentagon integrals.