The Weak Gravity Conjecture and Effective Field Theory

Abstract

The Weak Gravity Conjecture (WGC) is a proposed constraint on theories with gauge fields and gravity, requiring the existence of light charged particles and/or imposing an upper bound on the field theory cutoff $\Lambda$. If taken as a consistency requirement for effective field theories (EFTs), it rules out possibilities for model-building including some models of inflation. I demonstrate simple models which satisfy all forms of the WGC, but which through Higgsing of the original gauge fields produce low-energy EFTs with gauge forces that badly violate the WGC. These models illustrate specific loopholes in arguments that motivate the WGC from a bottom-up perspective; for example the arguments based on magnetic monopoles are evaded when the magnetic confinement that occurs in a Higgs phase is accounted for. This indicates that the WGC should not be taken as a veto on EFTs, even if it turns out to be a robust property of UV quantum gravity theories. However, if the latter is true then parametric violation of the WGC at low energy comes at the cost of non-minimal field content in the UV. I propose that only a very weak constraint is applicable to EFTs, $\Lambda \lesssim {\left(-\log g\right)}^{-1/2}{M}_{\text{pl}}$ where $g$ is the gauge coupling, motivated by entropy bounds. Remarkably, EFTs produced by Higgsing a theory that satisfies the WGC can saturate but not violate this bound.

27 pages, 3 figures, v2 with minor revisions and added references

References in corpus (13)

• On the Geometry of the String Landscape and the Swampland
• Causality, Analyticity and an IR Obstruction to UV Completion
• Symmetries and Strings in Field Theory and Gravity
• Natural inflation with multiple sub-Planckian axions
• The Weak Gravity Conjecture in three dimensions
• Natural Inflation and Quantum Gravity
• Infrared Consistency and the Weak Gravity Conjecture
• On the Possibility of Large Axion Moduli Spaces
• Nonperturbative Instability of AdS_5 x S^5/Z_k
• Oscillations in the inflaton potential?
• Natural and Multi-Natural Inflation in Axion Landscape
• Vacua Morghulis
• Natural Milli-Charged Inflation

Cited by in corpus (1)

• An Axion-induced SM/MSSM Higgs Landscape and the Weak Gravity Conjecture