The Weak Gravity Conjecture and Emergence from an Ultraviolet Cutoff

TL;DR

This work argues that ultraviolet cutoffs tied to the Weak Gravity Conjecture (WGC) and its Sublattice variant (sLWGC) are tightly linked: towers of charged states trigger concurrent strong-coupling scales for gauge fields and gravity, suggesting an emergent gauge sector from quantum gravity dynamics. For general gauge groups, the sLWGC implies parametric upper bounds on the quantum gravity scale that align with the gauge-theory strong-coupling scale, especially when the spectrum saturates the sLWGC. A converse claim shows that if gauge forces become strong at or below the quantum gravity scale, the WGC follows (up to order-one factors); further, gauge-gravity unification arguments extend to nonabelian and product groups, with Higgsing introducing nuanced caveats. The paper also discusses string-theory caveats, heavy spectra, and phenomenological implications, including nonabelian dark radiation and chromonatural inflation, illustrating how these UV cutoffs constrain high-scale physics.

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.

Figures (5)

• Figure 1: The nonabelian sLWGC (left) and abelian sLWGC (right) for an $\mathrm{SU}(2)$ gauge group. For a sublattice of fixed index, the nonabelian sLWGC requires many more particles charged under the $\mathrm{U}(1)$ Cartan below a given mass scale than the abelian sLWGC does, as the latter can be satisfied by particles charged under a sparse set of representations, provided they are sufficiently light.
• Figure 2: Higgsing in a lattice with $e_A^2 / e_B^2$ irrational. If the direction orthogonal to the Higgsed particle (shown in red) does not intersect any lattice points, then the WGC (and sLWGC) need not be satisfied in the resulting theory.
• Figure 3: Preservation of the WGC under Higgsing for a theory with a finitely generated convex hull. Since the convex hull condition is satisfied in the direction $\vec{e}_\perp$ orthogonal to the Higgsed particle (shown in red, with charge-to-mass vector $\vec{z}_0$), we necessarily have either $|\vec{z}_1 \cdot \vec{e}_\perp| \geq 1$ or $|\vec{z}_2 \cdot \vec{e}_\perp | \geq 1$. This ensures that one of these two particles will still satisfy the convex hull condition after Higgsing.
• Figure 4: (s)LWGC UV cutoff bound as a function of $g$ and $N$ (solid contours, labeled by representative physical scenarios). The dashed lines are benchmark choices of $g$ in two particular cosmological scenarios that favor small nonabelian gauge couplings.
• Figure 5: Contributions to four-photon scattering: at tree level, through graviton exchange at order $G_N$; at one loop, through electromagnetic interactions with charged particles at order $e^4$; at two loops, from one diagram of order $e^6$ and one of order $e^4 G_N$.