Infrared consistency and the weak gravity conjecture

Abstract

The weak gravity conjecture (WGC) asserts that an Abelian gauge theory coupled to gravity is inconsistent unless it contains a particle of charge q and mass m such that q ≥ m/m Pl . This criterion is obeyed by all known ultraviolet completions and is needed to evade pathologies from stable black hole remnants. In this paper, we explore the WGC from the perspective of low-energy effective field theory. Below the charged particle threshold, the effective action describes a photon and graviton interacting via higher-dimension operators. We derive infrared consistency conditions on the parameters of the effective action using i ) analyticity of light-by-light scattering, ii ) unitarity of the dynamics of an arbitrary ultraviolet completion, and iii ) absence of superluminality and causality violation in certain non-trivial backgrounds. For convenience, we begin our analysis in three spacetime dimensions, where gravity is non-dynamical but has a physical effect on photon-photon interactions. We then consider four dimensions, where propagating gravity substantially complicates all of our arguments, but bounds can still be derived. Operators in the effective action arise from two types of diagrams: those that involve electromagnetic interactions (parameterized by a charge-to-mass ratio q/m) and those that do not (parameterized by a coefficient γ). Infrared consistency implies that q/m is bounded from below for small γ.

α′ corrections of Reissner-Nordström black holes

“…Thus, not all the solutions of the Einstein-Maxwell theory can be embedded in the Heterotic Superstring effective action because unequal electric and magnetic charges always generate a non-trivial scalar field. quantum black hole physics is currently attracting much attention [19,34,35,31,36,37,32,20,33,38]. A recurrent assumption in these explorations is that no additional degrees of freedom are activated at higher orders.…”

Softness and amplitudes’ positivity for spinning particles

“…This ratio can still be taken very small but only in the trivial way g * 1, too. 17 This relation implies also that Λ is at most one-loop suppressed relative to g * M Planck .…”

“…This is why they have found several applications ranging e.g. from the a-theorem [3] to the theory of pions [4][5][6], from WW-scattering [1,7,8] to composite Higgs models [8][9][10][11], from quantum gravity [12] to inflation [13,14], from Galileons [15] to massive gravity [16], from the weak gravity conjecture [17,18] to the OPE coefficients [19], from the conformal blocks expansion [20] to the Mellin amplitudes for CFTs at large-N [21]. Virtually all literature have focused on positivity bounds for amplitudes of bosons with spin-0, -1 or -2; see [22] for an interesting exception that studied dimension-6 4-fermi interactions, and e.g.…”

Universal bounds on charged states in 2d CFT and 3d gravity

“…6 It is also possible to derive 4 See e.g. [21,25] for recent interesting arguments along these lines. In particular, all examples we present have a coupling for the gauge field that is O(1) at the Planck scale, whereas [21] argues for a stronger bound only when this gauge coupling is small.…”