Abstract
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 F2 ∧ H3 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.
Highlights
Symmetries have long played a major role in theoretical physics
We focus our discussion on the absence of ChernWeil global symmetries, one could rephrase much of the discussion in the language of cobordism
Much of the intricate structure of branes and their interactions within string theory can be viewed as providing a mechanism for removing potential global symmetries from the theory. This suggests that this structure could survive beyond the known string lampposts, as a general feature of theories of quantum gravity. Another pattern we have observed in Type II string theory and M-theory is that, while many Chern-Weil symmetries are broken by Chern-Simons couplings, in each example we find at least one current that is unbroken at the level of the bulk supergravity action, corresponding to the required branes of the highest dimension
Summary
Symmetries have long played a major role in theoretical physics. In recent years, it has been widely understood that the concept of symmetry is broader than previously recognized [1, 2], and the notion of a p-form generalized global symmetry has been introduced [3]. In a U(1) gauge theory, the existence of magnetic monopoles breaks the would-be Chern-Weil symmetry generated by F ∧F , so gauging this current via a Chern-Simons term of the form C ∧F ∧F is inconsistent. When these magnetic monopoles admit dyonic excitations, they have a compact scalar σ localized on their worldvolume, and a current of the form F ∧ F + δ3m ∧ dAσ is conserved and may be gauged.
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