The Weak Gravity Conjecture and Emergence from an Ultraviolet Cutoff

TL;DR

This paper explores the ultraviolet cutoffs related to the Weak Gravity Conjecture, establishing bounds on the strong gravity scale and suggesting gauge fields may emerge from quantum gravity effects.

Contribution

It derives a parametric upper bound on the strong gravity scale for arbitrary gauge theories and links the WGC to gauge field emergence from quantum gravity.

Findings

Upper bound on the strong gravity scale for gauge theories

Loop corrections from charged particles become significant at similar scales

Gauge fields may emerge from quantum gravity effects

Abstract

We study ultraviolet cutoffs associated with the Weak Gravity Conjecture (WGC) and Sublattice Weak Gravity Conjecture (sLWGC). There is a magnetic WGC cutoff at the energy scale $e G_N^{-1/2}$ with an associated sLWGC tower of charged particles. A more fundamental cutoff is the scale at which gravity becomes strong and field theory breaks down entirely. By clarifying the nature of the sLWGC for nonabelian gauge groups we derive a parametric upper bound on this strong gravity scale for arbitrary gauge theories. Intriguingly, we show that in theories approximately saturating the sLWGC, the scales at which loop corrections from the tower of charged particles to the gauge boson and graviton propagators become important are parametrically identical. This suggests a picture in which gauge fields emerge from the quantum gravity scale by integrating out a tower of charged matter fields. We derive a converse statement: if a gauge theory becomes strongly coupled at or below the quantum gravity scale, the WGC follows. We sketch some phenomenological consequences of the UV cutoffs we derive.