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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.

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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