Non-Invertible Symmetries from Discrete Gauging and Completeness of the Spectrum

TL;DR

The paper analyzes higher-form symmetries in gauge theories built from disconnected groups that incorporate charge conjugation. It demonstrates that pure gauge theories exhibit a non-invertible electric 1-form symmetry and automatically possess a $ obreak\eta Z_2$ dual $(d-2)$-form symmetry arising from $ obreak\eta\pi_0(G)$. String Theory embeddings of these gauge theories naturally host twist vortices (Alice strings) that break the $(d-2)$-form symmetry, in line with the Swampland expectation of no global symmetries in quantum gravity. The results illuminate how non-invertible higher-form symmetries arise ubiquitously in higher dimensions for disconnected gauge groups and connect (via brane constructions) to anomalies and symmetry breaking patterns, with potential implications for the structure of quantum gravity and Swampland conjectures.

Abstract

We study global 1- and $(d-2)$-form symmetries for gauge theories based on disconnected gauge groups which include charge conjugation. For pure gauge theories, the 1-form symmetries are shown to be non-invertible. In addition, being the gauge groups disconnected, the theories automatically have a $\mathbb{Z}_2$ global $(d-2)$-form symmetry. We propose String Theory embeddings for gauge theories based on these groups. Remarkably, they all automatically come with twist vortices which break the $(d-2)$-form global symmetry. This is consistent with the conjectured absence of global symmetries in Quantum Gravity.