Abstract
Axions with broken discrete shift symmetry (axion monodromy) have recently played a central role both in the discussion of inflation and the `relaxion' approach to the hierarchy problem. We suggest a very minimalist way to constrain such models by the weak gravity conjecture for domain walls: While the electric side of the conjecture is always satisfied if the cosine-oscillations of the axion potential are sufficiently small, the magnetic side imposes a cutoff, $\Lambda^3 \sim m f M_{pl}$, independent of the height of these `wiggles'. We compare our approach with the recent related proposal by Ibanez, Montero, Uranga and Valenzuela. We also discuss the non-trivial question which version, if any, of the weak gravity conjecture for domain walls should hold. In particular, we show that string compactifications with branes of different dimensions wrapped on different cycles lead to a `geometric weak gravity conjecture' relating volumes of cycles, norms of corresponding forms and the volume of the compact space. Imposing this `geometric conjecture', e.g.~on the basis of the more widely accepted weak gravity conjecture for particles, provides at least some support for the (electric and magnetic) conjecture for domain walls.
Highlights
Very recently, developing an idea of [43], the authors of [54] have applied the WGC for domain walls to axion monodromy, albeit mainly in the different context of the relaxion proposal
We suggest a very minimalist way to constrain such models by the weak gravity conjecture for domain walls: while the electric side of the conjecture is always satisfied if the cosine-oscillations of the axion potential are sufficiently small, the magnetic side imposes a cutoff, Λ3 ∼ mf Mpl, independent of the height of these ‘wiggles’
We show that string compactifications with branes of different dimensions wrapped on different cycles lead to a ‘geometric weak gravity conjecture’ relating volumes of cycles, norms of corresponding forms and the volume of the compact space
Summary
We aim at obtaining constraints on models based on axion monodromy (inflation or relaxation). We begin by pointing out the existence of light domain walls in those models. These are different from the membranes inherent to the KS approach to axion monodromy. They belong purely to the effective field theory regime and do not descend from a higher dimensional gauge theory. We apply the WGC to these low energy domain walls and discuss the relation of our result to the recent analysis of [54]
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