Abstract
The Weak Gravity Conjecture (WGC) bounds the mass of a particle by its charge. It is expected that this bound can not be below the ultraviolet cut-off scale of the effective theory. Recently, an extension of the WGC was proposed in the presence of scalar fields. We show that this more general version can bound the mass of a particle to be arbitrarily far below the ultraviolet cut-off of the effective theory. It therefore manifests a form of hierarchical UV/IR mixing. This has possible implications for naturalness. We also present new evidence for the proposed contribution of scalar fields to the WGC by showing that it matches the results of dimensional reduction. In such a setup the UV/IR mixing is tied to the interaction between the WGC and non-local gauge operators.
Highlights
Since (1.2) is tied to quantum gravity physics, with an associated mass scale ΛUV, but is a constraint on an arbitrarily low IR scale, it manifests a form of UV/IR mixing
In this note we proposed that in the presence of scalar fields the general version of the Weak Gravity Conjecture (WGC) (1.2) can bound the mass of the WGC particle far below the UV cut-off scale of the effective theory
Such a bound on an IR mass from UV quantum gravity physics is interesting in that it manifests a form of UV/IR mixing
Summary
We present new evidence for (2.3) based on dimensional reduction. The point is that the WGC (2.1) in 5 dimensions leads, upon a classical dimensional reduction, to the generalised version of the WGC (2.3) in 4 dimensions. we will consider a classical dimensional reduction. As discussed in the introduction, at the quantum level it is difficult to control β and the mass of the scalar mediators. This example model is no exception to this, and quantum corrections can significantly modify the scenario. The bound on its mass from the 5-dimensional WGC reads (see for example [15]) If we reduce this theory on a circle, we get an effective 4-dimensional action for the zero modes. The 4-dimensional fields are the dilaton φ, an axion a, a complex scalar h, the graviphoton Aμ0 , and the zero mode of the gauge field Aμ1. The axion a originates from the extra-dimensional component of the gauge field a = S1 A4.
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