Nonlocal gravitational effective actions must satisfy a set of interlocking constraints to preserve unitarity so that probabilities add to one and the quantum S matrix remains well defined. Central requirements are the no-ghost condition that forbids new negative-residue poles in propagators, analyticity of form factors in the complex momentum plane consistent with dispersion relations, spectral positivity of the Källén Lehmann representation, and compatibility with the optical theorem or Cutkosky rules so that loop discontinuities match physical intermediate states. John F. Donoghue at University of Massachusetts Amherst frames these demands within the effective field theory perspective showing that low energy gravitational amplitudes must respect unitarity order by order up to the EFT cutoff, and that apparent nonlocal operators must not introduce pathological degrees of freedom that would violate probability conservation.
Analytic and spectral requirements
Analyticity and spectral properties control where and how nonlocal modifications can appear. Nonlocal form factors like entire functions of the d Alembertian are often chosen to avoid new poles and thereby satisfy the no-ghost condition. The spectral density must remain positive so physical states carry positive norm, otherwise perturbative instabilities and negative probabilities follow. Research on scattering and information flow by Steven B. Giddings at University of California Santa Barbara emphasizes that maintaining the correct analytic structure is essential for scattering amplitudes to obey the optical theorem and for semiclassical descriptions of black holes to remain consistent with unitarity. Violations of these analytic or spectral constraints typically produce runaway instabilities or contradictions with experimentally constrained low energy behavior.
Causality, boundary choices, and EFT control
Causality and the choice of boundary conditions for nonlocal operators are equally decisive. Implementing retarded or causal Green functions prevents acausal signal propagation that would undermine the physical interpretation of amplitudes. Practical model building also requires careful EFT control because loop corrections can reintroduce problematic poles or cuts unless the nonlocality is defined with a consistent UV completion or justified resummation. Consequences extend beyond formal consistency: cosmological model building, gravitational wave propagation, and proposals for black hole evaporation are all sensitive to whether nonlocal modifications respect unitarity. The distribution of research effort across institutions in North America and Europe reflects differing emphases on observational consequences versus formal constraints, but the common thread is that unitarity, analyticity, spectral positivity, and causality together enforce unitarity in nonlocal gravitational effective actions.