Dual conformal constraints and infrared equations from global residue theorems in N=4 SYM theory

TL;DR

This paper explores how global residue theorems in the Grassmannian formulation of N=4 super Yang-Mills theory encode infrared equations and dual conformal constraints, revealing deep geometric structures behind amplitude relations.

Contribution

It demonstrates that infrared equations and dual conformal constraints are explicitly derived from global residue theorems in the Grassmannian framework, linking amplitude relations to geometric residue identities.

Findings

Infrared equations are implied by global residue theorems.

Dual conformal constraints are mapped to specific residue theorems.

The BCFW and parity-conjugated amplitude relation emerges from residue identities.

Abstract

Infrared equations and dual conformal constraints arise as consistency conditions on loop amplitudes in N=4 super Yang-Mills theory. These conditions are linear relations between leading singularities, which can be computed in the Grassmannian formulation of N=4 super Yang-Mills theory proposed recently. Examples for infrared equations have been shown to be implied by global residue theorems in the Grassmannian picture. Both dual conformal constraints and infrared equations are mapped explicitly to global residue theorems for one-loop next-to-maximally-helicity-violating amplitudes. In addition, the identity relating the BCFW and its parity-conjugated form of tree-level amplitudes, is shown to emerge from a particular combination of global residue theorems.