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 $\Lambda_{\rm new} \sim (e m M_{\rm pl})^{1/2}$, 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 emphasise 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 not in conflict with standard UV completions, including weakly coupled ones.
Highlights
Lower bounds on Wilson coefficients [27–31] in certain cases ruling out classes of theories from having a standard UV completion such as weakly broken Galileon theories [27, 28]
Where overall positivity is still ensured by the sum over ‘unknown’ configurations f. It is in the application of improved positivity bounds that our results will differ from previous discussions of positivity bound for QED coupled to gravity, notably [40], and more recently [41–43] which have focused entirely on the gravitational Euler-Heisenberg effective field theory that describes physics well below the electron mass1
This parallels some of the discussion in what follows for 4D, we shall make use of the improved positivity bounds which allows us to infer a bound on the cutoff of the effective field theories (EFTs) and avoid the need to focus on the high powers of s in the expansion of the amplitude
Summary
In the following we consider the theory of QED minimally coupled to gravity, which is itself a low energy EFT. The action for the fermionic (spinor) QED reads. Where ψ is the Dirac field, ψ ≡ ψ†γ0, ∇/ ≡ γμ∇μ, and γμ = vaμγa are the gamma matrices, vμa the vierbein, and ∇ the covariant derivative with the spin-connection (see appendix B.1). We denote by m and e the electron mass and charge respectively. When the role of the electron is played by a complex scalar field, the action for scalar QED is . Where φ is the complex scalar and the gauge-covariant derivative is defined as usual Dμ ≡ ∂μ −ieAμ. Throughout this work we use mostly plus signature (−, +, +, +)
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
