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The Weak Gravity Conjecture and Effective Field Theory

Prashant Saraswat

TL;DR

The paper questions the notion that the Weak Gravity Conjecture (WGC) universally constrains low-energy effective field theories (EFTs). By constructing a UV theory that satisfies the WGC and then Higgsing it to a low-energy theory, the author shows that the resulting EFT can violate the standard WGC bounds while still respecting an entropy-based bound on the cutoff scale. The analysis reveals loopholes in bottom-up WGC arguments, particularly for magnetic monopole reasoning and multi-field generalizations, and argues that the robust constraint for EFTs is a weaker bound tied to entropy considerations, which can be saturated but not violated if the UV theory satisfies the multifield WGC. These insights have practical implications for model-building, especially in inflationary scenarios like extranatural inflation and bi-axion constructions, where UV-consistent Higgsing can yield viable large-field dynamics within a controlled EFT. Overall, the work reframes the role of the WGC in EFTs as a guide to UV consistency and minimality rather than an absolute veto, emphasizing the primacy of entropy-based constraints for low-energy theories.

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 $Λ$. 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, $Λ\lesssim \left(-\log g \right)^{-1/2} M_\text{pl}$ 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.

The Weak Gravity Conjecture and Effective Field Theory

TL;DR

The paper questions the notion that the Weak Gravity Conjecture (WGC) universally constrains low-energy effective field theories (EFTs). By constructing a UV theory that satisfies the WGC and then Higgsing it to a low-energy theory, the author shows that the resulting EFT can violate the standard WGC bounds while still respecting an entropy-based bound on the cutoff scale. The analysis reveals loopholes in bottom-up WGC arguments, particularly for magnetic monopole reasoning and multi-field generalizations, and argues that the robust constraint for EFTs is a weaker bound tied to entropy considerations, which can be saturated but not violated if the UV theory satisfies the multifield WGC. These insights have practical implications for model-building, especially in inflationary scenarios like extranatural inflation and bi-axion constructions, where UV-consistent Higgsing can yield viable large-field dynamics within a controlled EFT. Overall, the work reframes the role of the WGC in EFTs as a guide to UV consistency and minimality rather than an absolute veto, emphasizing the primacy of entropy-based constraints for low-energy theories.

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 . 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, where 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.

Paper Structure

This paper contains 10 sections, 7 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction & Synopsis
  2. Bottom-up arguments for a Weak Gravity Conjecture
  3. "Electric" form
  4. "Magnetic" form
  5. The generalized (multi-field) WGC
  6. Higgsing to Violate the WGC
  7. Implications for model-building
  8. A Proposed Bound on Gauge EFTs
  9. Conclusions
  10. The Electric WGC and Large Field Inflation

Figures (3)

  • Figure 1: Spectrum of charged particles (blue) and gauge fields (red) for the model of section \ref{['sec:higgs']}, along with the mass scales implied by the WGC (black). This spectrum satisfies the various WGCs for the $A$ and $B$ fields when the scalar of charge $(Z,1)$ does not have a vev. However, when the $(Z,1)$ field acquires a vev, then most forms of the WGC (see Table \ref{['tab:wgc']}) are violated for the remaining massless gauge field, which has coupling $g_\text{eff} = g/Z$.
  • Figure 2: Magnetic monopoles of the $A, B$ gauge fields in the two phases of the model. Left: In the Coulomb phase, the magnetic WGC requires that magnetic monopoles of both the $A$ and $B$ fields exist, with magnetic charge $2\pi/g$ and size of order the cutoff length $\Lambda^{-1}$, where $\Lambda \lesssim g M_\text{pl}$. Right: In the Higgs phase where a scalar of charge $(Z, 1)$ gets a vev, magnetic flux of the massive gauge boson $A + B/Z$ is confined, and only net $B - A/Z$ flux can escape to infinity. A monopole of $B - A/Z$ charge can be formed by joining $Z$ monopoles of $B$ and one anti-monopole of $A$, with the $A + B/Z$ field confined to flux tubes.
  • Figure 3: A sketch of a possible inflaton potential generated within the bi-axion models discussed here and in delaFuente:2014aca, for an EFT cutoff that is only slightly above the compactification scale. In this case the potential may receive a suppressed 'higher harmonic" contribution with a period $1/Z$ times the total field range, leading to observable oscillations in the primordial power spectrum. (The amplitude of this contribution is exaggerated in this figure; current data constrains it to be smaller than pictured.)