On-shell recursion and soft theorems for worldline quantum field theory
Abstract
We derive a set of on-shell recursion relations for amplitudes in worldline quantum field theory (WQFT), an effective theory of gravity coupled to a massive worldline which is relevant for computing classical gravitational observables. We overcome the poor large-z falloff of amplitudes under an all-line complex momentum deformation by deriving and exploiting a new soft-graviton theorem in the presence of a worldline. This theorem generalizes the leading (Weinberg) and subleading soft theorems with additional contributions due to soft emission from the worldline. Our main result is a d-dimensional recursion formula, expressing any n-graviton rational amplitude in terms of lower-point amplitudes from WQFT and pure gravity. Using the soft-worldline theorem, we can obtain amplitudes with any number of external worldline fluctuations from the corresponding all-graviton amplitudes, making the recursion sufficient to construct any rational amplitude of the theory. We verify our results by explicitly computing two-graviton and three-graviton amplitudes.
Related
- Schwinger--Keldysh worldline effective field theory for quantum black holes: dissipation, noise and decoherence
- Irreversibility of quantum field theory in de Sitter: The C, F and A theorems
- Generalized unitarity method for worldline field theory
- Single-worldline theory for a dissipative Mott transition
- Bypassing no-go theorems on mixed classical-quantum systems: the (counter)example of hybrid van Hove theory
BibTeX
@misc{castet2026onshell,
title = {{On-shell recursion and soft theorems for worldline quantum field theory}},
author = {Nathan Castet and Vincent F He},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01714},
eprint = {2609.01714},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05742711v1},
}
RIS
TY - UNPB
TI - On-shell recursion and soft theorems for worldline quantum field theory
AU - Nathan Castet
AU - Vincent F He
PY - 2026
DA - 2026/09/08
PB - HAL
DO - 10.48550/arxiv.2609.01714
UR - https://hal.science/hal-05742711v1
AB - We derive a set of on-shell recursion relations for amplitudes in worldline quantum field theory (WQFT), an effective theory of gravity coupled to a massive worldline which is relevant for computing classical gravitational observables. We overcome the poor large-z falloff of amplitudes under an all-line complex momentum deformation by deriving and exploiting a new soft-graviton theorem in the presence of a worldline. This theorem generalizes the leading (Weinberg) and subleading soft theorems with additional contributions due to soft emission from the worldline. Our main result is a d-dimensional recursion formula, expressing any n-graviton rational amplitude in terms of lower-point amplitudes from WQFT and pure gravity. Using the soft-worldline theorem, we can obtain amplitudes with any number of external worldline fluctuations from the corresponding all-graviton amplitudes, making the recursion sufficient to construct any rational amplitude of the theory. We verify our results by explicitly computing two-graviton and three-graviton amplitudes.
ER -