Non-invertible symmetries from discrete gauging and completeness of the spectrum

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 ℤ2 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.