Photon-Graviton Amplitudes from the Effective Action

TL;DR

This paper calculates one-loop low-energy effective actions in Einstein-Maxwell theory with massive particles and derives explicit graviton-photon amplitudes, revealing their relation to photon-only amplitudes and establishing a gravitational Ward identity.

Contribution

It provides explicit formulas for one-graviton four-photon effective actions and one-graviton two-photon amplitudes, advancing understanding of quantum gravity effects in Einstein-Maxwell theory.

Findings

Explicit one-graviton four-photon effective action derived.

Explicit one-graviton two-photon amplitude obtained.

Gravitational Ward identity for graviton-photon amplitudes established.

Abstract

We report on the status of an ongoing effort to calculate the complete one-loop low-energy effective actions in Einstein-Maxwell theory with a massive scalar or spinor loop, and to use them for obtaining the explicit form of the corresponding M-graviton/N-photon amplitudes. We present explicit results for the effective actions at the one-graviton four-photon level, and for the amplitudes at the one-graviton two-photon level. As expected on general grounds, these amplitudes relate in a simple way to the corresponding four-photon amplitudes. We also derive the gravitational Ward identity for the 1PI one-graviton -- N photon amplitude.