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Supersymmetric Ward Identities and NMHV Amplitudes involving Gluinos

Steven J. Bidder, David C. Dunbar, Warren B. Perkins

TL;DR

The paper tackles the problem of deriving one-loop six-point NMHV amplitudes involving gluinos and adjoint scalars in $\mathcal{N}=4$ SYM without recomputing full loops. It uses Supersymmetric Ward Identities in combination with unitarity-based box-coefficient methods to generate fermionic and scalar amplitudes from known purely gluonic data, including cross-checks via quadruple cuts. The authors provide explicit all-two-gluino and all-two-scalar six-point NMHV box-coefficient structures and show how higher-fermion and scalar amplitudes follow from SWI and symmetry constraints. The work demonstrates a powerful symmetry-driven route to compact loop amplitudes with extended applicability to non-supersymmetric QCD and potentially to supergravity.

Abstract

We show how Supersymmetric Ward identities can be used to obtain amplitudes involving gluinos or adjoint scalars from purely gluonic amplitudes. We obtain results for all one-loop six-point NMHV amplitudes in $\NeqFour$ Super Yang-Mills theory which involve two gluinos or two scalar particles. More general cases are also discussed.

Supersymmetric Ward Identities and NMHV Amplitudes involving Gluinos

TL;DR

The paper tackles the problem of deriving one-loop six-point NMHV amplitudes involving gluinos and adjoint scalars in SYM without recomputing full loops. It uses Supersymmetric Ward Identities in combination with unitarity-based box-coefficient methods to generate fermionic and scalar amplitudes from known purely gluonic data, including cross-checks via quadruple cuts. The authors provide explicit all-two-gluino and all-two-scalar six-point NMHV box-coefficient structures and show how higher-fermion and scalar amplitudes follow from SWI and symmetry constraints. The work demonstrates a powerful symmetry-driven route to compact loop amplitudes with extended applicability to non-supersymmetric QCD and potentially to supergravity.

Abstract

We show how Supersymmetric Ward identities can be used to obtain amplitudes involving gluinos or adjoint scalars from purely gluonic amplitudes. We obtain results for all one-loop six-point NMHV amplitudes in Super Yang-Mills theory which involve two gluinos or two scalar particles. More general cases are also discussed.

Paper Structure

This paper contains 10 sections, 120 equations, 1 table.

Table of Contents

  1. Introduction
  2. ${\cal N} = 4$ Amplitudes and Recent Developments
  3. Supersymmetric Ward Identities
  4. Tree Amplitudes
  5. Six Point One Loop NMHV Amplitudes with two Gluinos
  6. Amplitudes With More Than Two Fermions
  7. Amplitudes Involving Scalars
  8. Conclusions
  9. Summary of One-Loop Two Gluino and Two Scalar Six-Point Amplitudes in ${\cal N} = 4$ SYM
  10. Graviton Scattering Amplitudes