Decompactification Limits of Non-Compact Gauge Theory

TL;DR

This paper explores whether non-compact gauge symmetries in quantum gravity can be broken by infinitely many fields, finding that such breaking often leads to decompactification or breakdown of the effective field theory.

Contribution

It demonstrates that breaking non-compact gauge symmetries with infinite fields results in decompactification or EFT breakdown, challenging the swampland conjecture.

Findings

Symmetries can be broken by infinite fields, but EFT breaks down.

Decompactification to higher dimensions can occur when breaking non-compact gauge symmetries.

Results impact the understanding of the swampland and the role of global symmetries in quantum gravity.

Abstract

The required absence of global symmetries in quantum gravity has been used to imply that all non-compact gauge theories are in the swampland. This argument stems from the idea that non-compact gauge symmetries always seem to be accompanied by global symmetries that cannot be broken with a finite number of fields. In this work, we investigate whether these symmetries can be broken by an uncountable infinity of fields. We find that the symmetries can be broken, but as soon as we add these fields the EFT breaks down and in some cases decompactifies to a higher-dimensional theory without the non-compact gauge symmetry, akin to undoing a Kaluza-Klein reduction on a non-compact space. We make various comments on the species scale, free parameters, and the Weak Gravity Conjecture along the way.