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Soft theorems in maximally supersymmetric theories

Zheng-Wen Liu

TL;DR

This work systematically derives and validates tree-level super soft theorems in maximize supersymmetry, focusing on $N=4$ SYM and $N=8$ SUGRA. It uses super-BCFW recursion to prove the theorems, decomposes amplitudes into MHV/NMHV sectors, and reveals that gravity soft operators arise as double copies of Yang–Mills operators, with explicit KLT-like relations. The authors provide extensive checks via explicit MHV/NMHV amplitudes and SUSY Ward identities, including soft gluino, gravitino, and gravi-photon divergences, and show vanishing of soft scalars in $N=8$ SUGRA. The results deepen understanding of soft limits in SUSY theories and illuminate the gauge-gravity double-copy structure at the level of soft theorems, with implications for symmetry interpretations and future explorations of soft dynamics in highly symmetric quantum field theories.

Abstract

In this paper we study the supersymmetric generalization of the new soft theorem which was proposed by Cachazo and Strominger recently. At tree level, we prove the validity of the super soft theorems in both ${\cal N}=4$ super-Yang-Mills theory and ${\cal N}=8$ supergravity using super-BCFW recursion relations. We verify these theorems exactly by showing some examples.

Soft theorems in maximally supersymmetric theories

TL;DR

This work systematically derives and validates tree-level super soft theorems in maximize supersymmetry, focusing on SYM and SUGRA. It uses super-BCFW recursion to prove the theorems, decomposes amplitudes into MHV/NMHV sectors, and reveals that gravity soft operators arise as double copies of Yang–Mills operators, with explicit KLT-like relations. The authors provide extensive checks via explicit MHV/NMHV amplitudes and SUSY Ward identities, including soft gluino, gravitino, and gravi-photon divergences, and show vanishing of soft scalars in SUGRA. The results deepen understanding of soft limits in SUSY theories and illuminate the gauge-gravity double-copy structure at the level of soft theorems, with implications for symmetry interpretations and future explorations of soft dynamics in highly symmetric quantum field theories.

Abstract

In this paper we study the supersymmetric generalization of the new soft theorem which was proposed by Cachazo and Strominger recently. At tree level, we prove the validity of the super soft theorems in both super-Yang-Mills theory and supergravity using super-BCFW recursion relations. We verify these theorems exactly by showing some examples.

Paper Structure

This paper contains 15 sections, 131 equations.

Table of Contents

  1. Introduction
  2. New soft graviton theorem and soft gluon theorem
  3. Cachazo-Strominger's new soft graviton theorem
  4. Soft gluon theorem in Yang-Mills theory
  5. Gravity soft operators as double copy of Yang-Mills soft operators
  6. Soft theorem in ${\cal N}=4$ super-Yang-Mills theory
  7. Super soft theorem in ${\cal N}=4$ SYM
  8. MHV and NMHV Examples
  9. Super soft theorem in ${\cal N}=8$ supergravity
  10. Super soft theorem in ${\cal N}=8$ SUGRA
  11. MHV Examples
  12. SUGRA soft operators as double copy of SYM soft operators
  13. Conclusion and discussions
  14. Alternative derivation of soft theorem in ${\cal N}=4$ SYM
  15. Sub-sub-leading soft operator in ${\cal N}=8$ SUGRA