Bilocal phase operators in beta-deformed super Yang-Mills

TL;DR

This paper introduces a phase operator method to derive tree-level scattering amplitudes in beta-deformed super Yang-Mills theory, extending the understanding of deformed supersymmetric gauge theories and their symmetries.

Contribution

It develops a new phase operator technique to generate deformed superamplitudes and explores their algebraic and diagrammatic properties, including MHV expansion validity.

Findings

Derived explicit phase operator for beta-deformed amplitudes

Proved validity of MHV vertex expansion in deformed theory

Connected deformed amplitudes to non-planar multi-loop unitarity cuts

Abstract

We present tree-level scattering amplitudes in beta-deformed super Yang-Mills theory in terms of new generating functions, derived by construction of a phase operator and application thereof to the N = 4 superamplitudes. The technique is explicitly illustrated for the MHV and NMHV sectors. Along these lines we propose a phase representation of the N = 4 superconformal algebra realized on deformed amplitudes in the planar limit. Validity of the MHV vertex expansion is proven and a connection to non-planar multi-loop unitarity cuts is established. Our derivations are also compatible with the related gamma-deformation.