Confined monopoles and failure of the Lattice Weak Gravity Conjecture

Abstract: Almost all known theories of quantum gravity satisfy the Lattice Weak Gravity Conjecture (LWGC), which posits that a consistent theory of quantum gravity must have a superextremal particle at every site in the charge lattice. However, a number of theories have been observed to violate the LWGC; such theories exhibit only a (finite index) sublattice of superextremal particles. This paper aims to identify universal features and patterns associated with LWGC violation across numerous examples in effective field theory, string theory, and M-theory. Some of these examples have appeared previously in the literature, while others are novel. In all such examples, we observe that LWGC failure is accompanied by the existence of fractionally charged monopoles confined by flux tubes, where superextremal particles exist everywhere in the sublattice dual to the superlattice of fractional confined monopole charges. The confining flux tubes become light when the failure of the LWGC becomes more extreme, so monopoles deconfine in the limit where LWGC-violating particles become infinitely massive. We also identify similarities between these confined monopoles, non-invertible symmetries, and the Hanany-Witten effect.

Confined Monopoles and the Lattice Weak Gravity Conjecture

The presented paper explores the fascinating domain of the lattice weak gravity conjecture (LWGC) and its exceptions in various theoretical frameworks, particularly effective field theories, string theory, and M-theory. Central to the discussion is the phenomenon where some known quantum gravity theories do not conform to LWGC, a conjecture positing the existence of a superextremal particle at every charge lattice site.

Overview

The authors begin by contextualizing the weak gravity conjecture (WGC), which posits that in a quantum gravity theory coupled with a gauge theory, gravity should not hinder black holes from decaying, implying a particle exists with a charge-to-mass ratio at least equal to that of an extremal black hole. The LWGC extends this by asserting that every lattice site in a charge lattice should have an associated superextremal particle. Nevertheless, instances of LWGC violations exist where superextremal particles reside on a sublattice instead of every individual lattice site.

Key Findings

1. Confined Monopoles: The paper highlights that LWGC violations are linked to the presence of fractionally charged monopoles which are confined by flux tubes. The degree of LWGC violation correlates with how light these flux tubes become.
2. Sublattice Weak Gravity Conjecture (sLWGC): For theories exhibiting LWGC violations, there is usually a sublattice where the sLWGC holds, ensuring that there exist superextremal particles throughout this sublattice. Notably, the sublattice’s coarseness, or integer scaling factor, becomes a critical analysis point.
3. Relationship Between Monopoles and Non-invertible Symmetries: The research draws parallels between the physics of confined monopoles and non-invertible symmetries, though the connection remains speculative.
4. Successful Evaluation Across Multiple Examples: The proposed relationship between LWGC failures and confined monopoles is validated across various examples, including UV-complete models and more abstract effective field theories. Particularly in compactified dimensions or with discrete gauge group setups, like Wilson loops, this mechanism provides a comprehensive explanation for observed deviations from the full LWGC.

Implications

The research carries both theoretical and practical implications. Theoretically, it further refines our understanding of the weak gravity conjecture, adding layers of nuance in terms of global symmetries and monopole physics. Practically, the insights gathered could guide hypothesized models in quantum gravity aiming to synthesize the behaviors of known particle spectra with those peculiar to quantum gravity domains. This work underpins potential areas of exploration in string theory that may challenge or support the foundations of the WGC.

Future Directions

Given the foundational nature of the research, future work could:

• Explore other instances of conjecture failures with an eye on fractional magnetic charges.
• Examine if confining monopole mechanisms could inform symmetry-breaking processes in more complex gauge theories.
• Investigate if monopoles and flux tubes, linked to intricate field configurations, offer insights into high-energy cosmic events or analogous systems in condensed matter physics.

In summary, this paper provides a meticulous examination of confined monopoles as a significant mechanism behind LWGC violations, inviting further scrutiny of the theoretical constructs concerning quantum gravity and the role that global symmetries might play.