Abstract
In this note we show that models of natural inflation based on closed string axions are incompatible with the weak gravity conjecture (WGC). Specifically, we use T- duality in order to map the bounds on the charge-to-mass ratio of particles imposed by the WGC, to constraints on the ratio between instanton actions and axion decay constants. We use this connection to prove that if the WGC holds, even when multiple axions are present and mix with each other, one cannot have large axion decay constants while remaining in a regime of perturbative control. We also discuss the extension of the WGC to discrete symmetries and its possible impact on models with axion monodromy, and the distinction between the strong and mild versions of the WGC. We argue that, if the strong version is violated, the constraints on large field inflation can be evaded while still satisfying the mild one. Finally, we offer some speculations regarding the import of these results to the general theory of inflation.
Highlights
Moduli space by this subgroup, we find that the axion has a finite field range whose ‘radius’ is known as the ‘axion decay constant’
In this note we show that models of natural inflation based on closed string axions are incompatible with the weak gravity conjecture (WGC)
The WGC would imply that axions with large decay constants do not arise in perturbative regimes of theories of quantum gravity
Summary
We review the original formulation of the WGC and some of the arguments that support it [15]. Along the lines of [16], its generalization to the case in which there are multiple gauge fields, and speculate about the possibility of applying the WGC to discrete gauge symmetries. That the goal of this paper is not to critically address the validity of the conjecture, but rather to extract consequences from it and apply them to models of inflation. Whether the conjecture is a generic consistency requirement of quantum gravity is a question that will require further analysis
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