Abstract

The Swampland program aims to determine the constraints that an EFT must satisfy to be consistent with a UV completion in quantum gravity. One of the most important proposed constraints is the absence of global symmetries, meaning that any global symmetry must be gauged or broken. In this talk, I will discuss a class of generalized global symmetries, which we call “Chern-Weil global symmetries,” that arise ubiquitously in gauge theories. The Noether currents of these Chern-Weil global symmetries are given by wedge products of gauge field strengths and their conservation follows from Bianchi identities, so they are not easy to break. However, exact global symmetries should not be allowed in a consistent theory of quantum gravity, and how quantum gravity avoids them can teach us many things about the physics of UV consistent EFTs. In particular, I will explain how many familiar phenomena in string theory, such as axions, Chern-Simons terms, worldvolume degrees of freedom on extended objects, and branes ending on or dissolving in other branes, can be interpreted as consequences of the absence of Chern-Weil symmetries, suggesting that they might be general features of quantum gravity. Finally, I will also show how the absence of non-invertible global symmetries is in 1-to-1 correspondence with a complete charged spectrum for compact gauge groups.