Stable causality and microcausality for Drummond–Hathrell photons

A bstract Local superluminal photon propagation arises at $$ \mathcal{O}\left(\alpha /{m}_e^2\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>/</mml:mo> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mi>e</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mrow> </mml:mfenced> </mml:math> in the Drummond Hathrell (DH) effective action obtained by integrating out the electron in QED coupled to gravity. Whether such superluminality implies a genuine violation of causality in curved spacetime is subtle and remains conceptually nontrivial. In this work we revisit this question using two complementary and largely symmetry-independent diagnostics. First, we analyse the global causal structure of the effective (optical) metric governing DH photon propagation and identify conditions under which it remains stably causal, thereby excluding the formation of closed causal curves. Second, from a quantum-field-theoretic perspective, we examine microcausality by treating the gravitational background as a fixed Lorentz-breaking field and applying flat-spacetime analyticity bounds to the photon commutator within the geometric-optics regime of the EFT. For two representative examples, a circular photon orbit in Schwarzschild and a linear trajectory in a two-black-hole geometry, we find that, within the regime of validity of the DH effective theory, both diagnostics indicate that the superluminal photon propagation is causally benign. Our results do not constitute a general definition of microcausality in curved spacetime, but provide a controlled and instructive check of causal consistency for EFT superluminality in gravitational backgrounds.