Compactness of gauge symmetries in quantum gravity

Establish that continuous gauge groups in consistent quantum gravity are compact, thereby ensuring that electric charge spectra form lattices.

Background

The authors discuss charge lattices and note that compactness of the gauge group implies a lattice of allowed charges. They flag the compactness of gauge symmetries as a swampland conjecture, which underpins charge lattice structure used throughout their analysis.

References

The charges form a lattice if the gauge group is compact (e.g., U(1)N), where the compactness of the gauge group is yet another swampland conjecture [Banks:2010zn].

— Proving the Weak Gravity Conjecture in Perturbative String Theory, Part I: The Bosonic String (2401.14449 - Heidenreich et al., 25 Jan 2024) in Section 1 (Introduction), footnote to the charge lattice discussion