QED positivity bounds

Abstract

We apply positivity bounds directly to a Uð1Þ 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 Λ new ∼ ðemM Pl Þ 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.

The FL bound and its phenomenological implications

“…and all 2d modes whose effective masses are H satisfy the rotating version of the FL bound (although a mass of order Hubble means the corresponding field is close to saturating 7 This is reminiscent of the proposed bound Λ EFT ≤ √ gmMP for pure QED in [33,34]. In this case too the charge carriers provide a (much stronger) upper bound on the EFT cut-off scale, albeit stemming from non-trivial assumptions about the scattering amplitudes.…”

Sharp boundaries for the swampland

“…Similar positive sum rules incorporating gravity were written down before, see e.g. [8,[25][26][27][28][29] (or [30] for the similar case of U(1) gauge theory). There is however a notorious obstacle in deriving bounds that involve the Newton constant G: the graviton propagator diverges in the limit of forward scattering (u → 0 in our conventions), seemingly invalidating the application of the positivity constraints.…”

Dual EFT bootstrap: QCD flux tubes

“…To proceed further, we notice that the maximum is attained by picking ImW (z) = 0, which in turn using (2.20) implies ReW (z) = 0. 12 We are led to maximize the following functional over varying λ 2…”

“…Many works have exploited positivity, including: the original studies in the context of the chiral Lagrangian [2][3][4], many interesting applications on RG-flows and the phenomenology of EFT interactions, see e.g. [5][6][7][8][9][10][11][12][13][14][15], as well as new developments [16][17][18][19][20][21][22][23].…”