Scattering Amplitudes and BCFW in $\mathcal{N}=2^{\ast}$ Theory

TL;DR

This paper applies massive spinor helicity formalism and BCFW recursion to compute scattering amplitudes in $ ext{N}=2^*$ super-Yang-Mills theory, revealing the importance of boundary contributions at infinity for covariance.

Contribution

It introduces a method to compute Coulomb branch amplitudes in $ ext{N}=2^*$ theory using projections from $ ext{N}=4$ and analyzes boundary terms in BCFW shifts.

Findings

Some shifted amplitudes have poles at infinity.

Including residues at infinity restores little group covariance.

The approach extends amplitude calculations to Coulomb branch scenarios.

Abstract

We use massive spinor helicity formalism to study scattering amplitudes in $\mathcal{N}=2^*$ super-Yang-Mills theory in four dimensions. We compute the amplitudes at an arbitrary point in the Coulomb branch of this theory. We compute amplitudes using projection from $\mathcal{N}=4$ theory and write three point amplitudes in a convenient form using special kinematics. We then compute four point amplitudes by carrying out massive BCFW shifts of the amplitudes. We find some of the shifted amplitudes have a pole at $z=\infty$. Taking the residue at $z=\infty$ into account ensures little group covariance of the final result.