Towards a Swampland Global Symmetry Conjecture using Weak Gravity

TL;DR

The paper proposes a Swampland Global Symmetry Conjecture for gauge-derived approximate global U(1) symmetries arising from a U(1) gauge theory Higgsed by an axion. By merging an axion-gauged U(1) framework with the (axionic) Weak Gravity Conjecture and completeness, they bound instanton actions in terms of the 4d EFT cutoff $\Lambda$, yielding a universal lower bound on symmetry-violating operator coefficients: $\alpha \sim \exp(-S_I) \gtrsim \exp(-M_ ext{P}^2/\Lambda^2)$. They illustrate the mechanism with 4d and 5d toy models, discuss gravitational instantons and Euclidean branes in string theory, and compare with black-hole thermal arguments, finding a consistent parametric suppression across approaches. The work also identifies potential loopholes and lays out several formulations toward a general Swampland Global Symmetry Conjecture, highlighting both the promise and the need for further refinement. Overall, the results connect quantum-gravity constraints to low-energy EFTs via a common exponential suppression scale set by the Planck mass and the UV cutoff, informing the fate of approximate global symmetries in quantum gravity.

Abstract

It is widely believed and in part established that exact global symmetries are inconsistent with quantum gravity. One then expects that approximate global symmetries can be quantitatively constrained by quantum gravity or swampland arguments. We provide such a bound for an important class of global symmetries: Those arising from a gauged $U(1)$ with the vector made massive via Higgsing with an axion. The latter necessarily couples to instantons, and their action can be constrained, using both the electric and magnetic version of the axionic weak gravity conjecture, in terms of the cutoff of the theory. As a result, instanton-induced symmetry breaking operators with a suppression factor not smaller than $\exp(-M_{\rm P}^2/Λ^2)$ are present, where $Λ$ is a cutoff of the 4d effective theory. We provide a general argument and clarify the meaning of $Λ$. Simple 4d and 5d models are presented to illustrate this, and we recall that this is the standard way in which things work out in string compactifications with brane instantons. The relation of our constraint to bounds that can be derived from wormholes or gravitational instantons and to those motivated by black-hole effects at finite temperature are discussed, and we present a generalization of the Giddings-Strominger wormhole solution to the case of a gauge-derived $U(1)$ global symmetry. Finally, we discuss potential loopholes to our arguments.

Figures (2)

• Figure 1: A worldline of a charged particle ending at an instanton at $x_*$. Integrating over instanton positions $x_*$ induces a global-charge-violating operator.
• Figure 2: A 5d toy model with charged scalars confined to the two boundary-branes. In the presence of a $\sigma$-VEV, the bulk $U(1)$ gauge symmetry is broken but a global $U(1)$ survives.