Photon-Graviton Amplitudes from the Effective Action

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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.