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QED positivity bounds

Lasma Alberte1,*, Claudia de Rham1,2,†, Sumer Jaitly1,‡, and Andrew J. Tolley1,2,§

  • 1Theoretical Physics, Blackett Laboratory, Imperial College, London SW7 2AZ, United Kingdom
  • 2CERCA, Department of Physics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106, USA

  • *l.alberte@imperial.ac.uk
  • †c.de-rham@imperial.ac.uk
  • ‡sumer.jaitly14@imperial.ac.uk
  • §a.tolley@imperial.ac.uk
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Phys. Rev. D 103, 125020 – Published 22 June, 2021

DOI: https://doi.org/10.1103/PhysRevD.103.125020

Abstract

We apply positivity bounds directly to a U(1) gauge theory with charged scalars and charged fermions, i.e., QED, minimally coupled to gravity. Assuming that the massless t-channel pole may be discarded, we show that the improved positivity bounds are violated unless new physics is introduced at the parametrically low scale Λnew∼(emMPl)1/2, consistent with similar results for scalar field theories, far lower than the scale implied by the weak gravity conjecture. This is sharply contrasted with previous treatments which focus on the application of positivity bounds to the low energy gravitational Euler-Heisenberg effective theory only. We emphasize that the low cutoff is a consequence of applying the positivity bounds under the assumption that the pole may be discarded. We conjecture an alternative resolution that a small amount of negativity, consistent with decoupling limits, is allowed and is not in conflict with standard UV completions, including weakly coupled ones.

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Phys. Rev. D 103, 125020– Published 22 June, 2021
  • Received 29 January 2021
  • Accepted 24 May 2021
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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