Non-local positivity bounds: islands in Terra Incognita

Abstract

The requirements of unitarity and causality lead to significant constraints on the Wilson coefficients of an EFT expansion, known as positivity bounds. Their standard derivation relies on the crucial assumption of polynomial boundedness on the growth of scattering amplitudes in the complex energy plane, which is a property satisfied by local QFTs, and by weakly coupled string theory in the Regge regime. The scope of this work is to clarify the role of locality by deriving generalized positivity bounds under the assumption of exponential boundedness, typical of non-local QFTs where the Froissart-Martin bound is usually not satisfied. Using appropriately modified dispersion relations, we derive new constraints and find regions in the EFT parameter space that do not admit a local UV completion. Furthermore, we show that there exist EFTs that satisfy IR causality and at the same time can admit a non-local UV completion, provided that the energy scale of non-locality is of the same order or larger than the EFT cutoff. Finally, we provide an explicit example of an exponentially bounded amplitude that satisfies partial-wave unitarity and asymptotic causality.