Soft theorems for boostless amplitudes

Du, Zong-Zhe; Stefanyszyn, David

Abstract

We consider effective field theories (EFTs) of scalar fields with broken Lorentz boosts, which arise by taking the decoupling and flat-space limits of the EFT of inflation, and derive constraints that must be satisfied by the corresponding scattering amplitudes if there is an underlying non-linearly realised symmetry. We primarily concentrate on extended shift symmetries which depend on the space-time coordinates, and find that combinations of scattering amplitudes obey enhanced Adler zeros. That is, such combinations vanish as one external momentum is taken soft, with the rate at which they vanish dictated by the corresponding symmetry. In our soft theorem derivation, we pay particular care to the energy and momentum-conserving delta functions that arise due to space-time translations, and show that when acted upon by derivatives with respect to spatial momenta, they yield a tower of soft theorems which are ultimately required for closure of the underlying symmetry algebra. All of our soft theorems correspond to constraints that must be satisfied by on-shell amplitudes and, even for symmetries that depend on the time coordinate, our soft theorems only require derivatives to be taken with respect to spatial momenta. We perform a soft bootstrap procedure to find solutions to our soft theorems, and compare these solutions to what we find from an off-shell analysis using the coset construction.

Citation

Du, Z.-Z., & Stefanyszyn, D. (2024). Soft theorems for boostless amplitudes. Journal of High Energy Physics, 2024(7), Article 11. https://doi.org/10.1007/jhep07%282024%29011

• Journal Article Type: Article
• Acceptance Date: Jun 5, 2024
• Online Publication Date: Jul 2, 2024
• Publication Date: Jul 2, 2024
• Deposit Date: Jul 24, 2024
• Publicly Available Date: Jul 24, 2024
• Journal: Journal of High Energy Physics
• Electronic ISSN: 1029-8479
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 2024
• Issue: 7
• Article Number: 11
• DOI: https://doi.org/10.1007/jhep07%282024%29011
• Keywords: Cosmological models, Space-Time Symmetries, Scattering Amplitudes, Effective Field Theories
• Public URL: https://nottingham-repository.worktribe.com/output/37139607
• Publisher URL: https://link.springer.com/article/10.1007/JHEP07(2024)011
• Additional Information: Received: 24 April 2024; Accepted: 5 June 2024; First Online: 2 July 2024