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  • Letter
  • Open Access

Nonlocal positivity bounds: Islands in terra incognita

Luca Buoninfante1,*, Long-Qi Shao2,3,4,†, and Anna Tokareva2,5,6,‡

  • *Contact author: luca.buoninfante@ru.nl
  • †Contact author: shaolongqi22@mails.ucas.ac.cn
  • ‡Contact author: tokareva@ucas.ac.cn
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Phys. Rev. D 112, L021904 – Published 28 July, 2025

DOI: https://doi.org/10.1103/37kc-25s3

Abstract

The requirements of unitarity and causality lead to significant constraints on the Wilson coefficients of an effective field theory (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 quantum field theories (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 nonlocal 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 nonlocal UV completion, provided that the energy scale of nonlocality 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.

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Phys. Rev. D 112, L021904– Published 28 July, 2025
  • Received 19 February 2025
  • Accepted 10 June 2025
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