Tidal effects in quantum field theory

TL;DR

This work addresses finite-size tidal effects in gravity by constructing a complete, non-redundant action for a real scalar coupled to two Weyl tensors using the Hilbert series. The authors compute all spinless tidal contributions at the leading post-Minkowskian order by exploiting a heavy-limit to isolate classical one-loop amplitudes, and they derive the associated $O(G^{2})$ tidal corrections to the Hamiltonian and scattering angle. The approach yields explicit, matched results with existing literature (e.g., Cheung 2020, Kalin 2020) and clarifies the role of operator basis choices and $ abla$-power counting in the classical limit. They also outline natural extensions to higher-curvature operators and spin effects, which could further illuminate the EFT structure of gravitational tidal interactions.

Abstract

We apply the Hilbert series to extend the gravitational action for a scalar field to a complete, non-redundant basis of higher-dimensional operators that is quadratic in the scalars and the Weyl tensor. Such an extension of the action fully describes tidal effects arising from operators involving two powers of the curvature. As an application of this new action, we compute all spinless tidal effects at the leading post-Minkowskian order. This computation is greatly simplified by appealing to the heavy limit, where only a severely constrained set of operators can contribute classically at the one-loop level. Finally, we use this amplitude to derive the $\mathcal{O}(G^{2})$ tidal corrections to the Hamiltonian and the scattering angle.

Figures (1)

• Figure 1: The only topology contributing classical tidal effects at one loop. The tidal effects of particle 1 are probed. The wavy lines represent either photons or gravitons.