Chern-Weil Global Symmetries and How Quantum Gravity Avoids Them

Understand

We draw attention to 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, such as $F_2 \wedge H_3$ and $\text{tr}(F_2^2)$, and their conservation follows from Bianchi identities.
• As a result, they are not easy to break.
• However, it is widely believed that exact global symmetries are not allowed in a consistent theory of quantum gravity.