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Double Soft Theorem for Perturbative Gravity

Arnab Priya Saha

TL;DR

The paper derives a double soft graviton theorem within perturbative gravity using the CHY framework, showing that the leading double-soft limit of gravity amplitudes is captured by a universal factor $S^{*(0)}$ at order $1/\tau$ when two gravitons become soft. It demonstrates that, for gravity, CHY reproduces the local, same-leg emission contributions and that nonlocal, multi-leg soft processes appear in full Feynman-diagram analyses but are not contained in the CHY double-soft expression. The Einstein-Maxwell warm-up confirms the CHY–Lagrangian correspondence for EM, while the gravity analysis clarifies how the CHY integrand encodes the gravity vertices and how gauge invariance is preserved. The work suggests further exploration of loop corrections and potential ties to asymptotic symmetries beyond the BMS framework.

Abstract

Following up on the recent work of Cachazo, He and Yuan \cite{arXiv:1503.04816 [hep-th]}, we derive the double soft graviton theorem in perturbative gravity. We show that the double soft theorem derived using CHY formula precisely matches with the perturbative computation involving Feynman diagrams. In particular, we find how certain delicate limits of Feynman diagrams play an important role in obtaining this equivalence.

Double Soft Theorem for Perturbative Gravity

TL;DR

The paper derives a double soft graviton theorem within perturbative gravity using the CHY framework, showing that the leading double-soft limit of gravity amplitudes is captured by a universal factor at order when two gravitons become soft. It demonstrates that, for gravity, CHY reproduces the local, same-leg emission contributions and that nonlocal, multi-leg soft processes appear in full Feynman-diagram analyses but are not contained in the CHY double-soft expression. The Einstein-Maxwell warm-up confirms the CHY–Lagrangian correspondence for EM, while the gravity analysis clarifies how the CHY integrand encodes the gravity vertices and how gauge invariance is preserved. The work suggests further exploration of loop corrections and potential ties to asymptotic symmetries beyond the BMS framework.

Abstract

Following up on the recent work of Cachazo, He and Yuan \cite{arXiv:1503.04816 [hep-th]}, we derive the double soft graviton theorem in perturbative gravity. We show that the double soft theorem derived using CHY formula precisely matches with the perturbative computation involving Feynman diagrams. In particular, we find how certain delicate limits of Feynman diagrams play an important role in obtaining this equivalence.

Paper Structure

This paper contains 18 sections, 48 equations, 6 figures.

Table of Contents

  1. Introduction
  2. A Brief Review of CHY Formula and Weinberg Soft Theorem
  3. Scattering Amplitude
  4. Single Soft Limit
  5. Double Soft Limit of CHY Formula
  6. Double Soft Limit for Einstein Maxwell Theory
  7. Feynman Diagrams
  8. Double Soft Limit in Gravity Amplitude
  9. Remarks on the double soft factor:
  10. Double Soft Limit from Feynman Diagrams for Gravity
  11. Discussion and Conclusion
  12. Acknowledgements
  13. Appendix
  14. Derivation of Eq.(\ref{['grav ds Pf expansion']})
  15. Derivation of Double Soft Factor
  16. ...and 3 more sections

Figures (6)

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  • ...and 1 more figures