Chern-Weil global symmetries and how quantum gravity avoids them

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 boolean AND H-3 and 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. As a result, any Chern-Weil global symmetry in a low-energy effective field theory must be either broken or gauged when the theory is coupled to gravity. In this paper, we explore the processes by which Chern-Weil symmetries may be broken or gauged in effective field theory and string theory. We will see that many familiar phenomena in string theory, such as axions, Chern-Simons terms, worldvolume degrees of freedom, and branes ending on or dissolving in other branes, can be interpreted as consequences of the absence of Chern-Weil symmetries in quantum gravity, suggesting that they might be general features of quantum gravity. We further discuss implications of breaking and gauging Chern-Weil symmetries for particle phenomenology and for boundary CFTs of AdS bulk theories. Chern-Weil global symmetries thus offer a unified framework for understanding many familiar aspects of quantum field theory and quantum gravity.

Automated summary

Chern-Weil global symmetries are a class of generalized global symmetries that are ubiquitous in gauge theories, characterized by Noether currents given by wedge products of gauge field strengths and difficult to break. It is believed that these symmetries are not allowed in a consistent theory of quantum gravity, leading to the necessity of breaking or gauging them when the theory is coupled to gravity. This paper explores the ways in which Chern-Weil symmetries may be broken or gauged in effective field theory and string theory, showing that familiar phenomena in string theory could be consequences of the absence of Chern-Weil symmetries in quantum gravity.