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We draw attention to a class of generalized global symmetries, which we call"Chern-Weil global symmetries," that arise ubiquitously in gauge theories. TheNoether currents of these Chern-Weil global symmetries are given by wedgeproducts of gauge field strengths, such as $F_2 \wedge H_3$ and$\text{tr}(F_2^2)$, and their conservation follows from Bianchi identities. Asa result, they are not easy to break. However, it is widely believed that exactglobal symmetries are not allowed in a consistent theory of quantum gravity. Asa result, any Chern-Weil global symmetry in a low-energy effective field theorymust be either broken or gauged when the theory is coupled to gravity. In thispaper, we explore the processes by which Chern-Weil symmetries may be broken orgauged in effective field theory and string theory. We will see that manyfamiliar phenomena in string theory, such as axions, Chern-Simons terms,worldvolume degrees of freedom, and branes ending on or dissolving in otherbranes, can be interpreted as consequences of the absence of Chern-Weilsymmetries in quantum gravity, suggesting that they might be general featuresof quantum gravity. We further discuss implications of breaking and gaugingChern-Weil symmetries for particle phenomenology and for boundary CFTs of AdSbulk theories. Chern-Weil global symmetries thus offer a unified framework forunderstanding many familiar aspects of quantum field theory and quantumgravity.

Chern-Weil Global Symmetries and How Quantum Gravity Avoids Them