Causality of Effective Field Theories in Gravitational Spacetimes

Abstract

Causality, along with unitarity, can be used to bound EFT coefficients of various EFTs. Here, we use microcausality and the Paley-Wiener theorem to bound the EFT coefficients of the scalar Goldstone boson as well as the Euler-Heisenberg effective action. These bounds on the coefficients match the bounds derived independently by imposing subluminality of the group velocity. We then show when microcausality-related bounds are equivalent to the subluminality of group velocity. In general, subluminal group velocity is a stronger condition when compared to microcausality. We would also like to extend causality analysis on EFTs on flat spacetime to EFTs on curved spacetime when they show superluminality. Here, we specifically look at the Drummond-Hathrell (DH) effective action. Local superluminal photon propagation arises at $\mathcal{O}(\alpha/m_e^2)$ in the 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, we treat the gravitational background to be a non-dynamical Lorentz-breaking field with a non-zero vacuum expectation value, and apply the microcausality bounds in flat spacetime on the photon propagator in the EFT-geometrical optics regime. 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. These checks 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.