Bound States in Perturbative Quantum Gravity with Hydrogen-like Degeneracy

@misc{jones2026bound,
  title = {{Bound States in Perturbative Quantum Gravity with Hydrogen-like Degeneracy}},
  author = {Callum R. T. Jones and Shruti Paranjape and Marcos Skowronek},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.29402},
  eprint = {2608.29402},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29402},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Bound States in Perturbative Quantum Gravity with Hydrogen-like Degeneracy
AU  - Callum R. T. Jones
AU  - Shruti Paranjape
AU  - Marcos Skowronek
PY  - 2026
DA  - 2026/10/10
PB  - arXiv
DO  - 10.48550/arxiv.2608.29402
UR  - https://arxiv.org/abs/2608.29402
AB  - Recent results in the study of gravitational scattering amplitudes indicate that some highly-symmetric relativistic systems may exactly conserve a version of the Laplace-Runge-Lenz (LRL) vector in two-body bound states. We make a systematic study, in the context of a generic EFT of long-range interactions due to the exchange of massless mediator particles of spins 0, 1/2, 1, 3/2, 2, of the conditions for the conservation of a hidden LRL vector; both classically (no orbital precession) and quantum-mechanically (hydrogen-like degeneracy of bound states). The calculations require several new technical developments including the extension of relativistic post-Minkowskian potential matching to quantum corrections and the incorporation of long-range forces due to the exchange of pairs of massless fermions. We find that while classically the absence of precession is a generic property of a large class of models, including Kaluza-Klein theories, with vector and scalar exchanges, maintaining the degeneracy quantum-mechanically requires a surprising cancellation between gravitons and 6 Majorana gravitinos, hinting at a special role for 𝒩=6 supergravity.
ER  -