Chern-Weil Global Symmetries and How Quantum Gravity Avoids Them

TL;DR

This paper investigates a class of generalized global symmetries called Chern-Weil symmetries, their resistance to breaking in gauge theories, and how quantum gravity inherently avoids them through mechanisms like gauging or breaking, with implications for string theory and holography.

Contribution

It introduces Chern-Weil global symmetries, analyzes their behavior in quantum gravity, and connects them to phenomena in string theory, providing a unified framework for understanding their absence.

Findings

Chern-Weil symmetries are conserved due to Bianchi identities.

Quantum gravity prevents exact Chern-Weil global symmetries by breaking or gauging them.

String theory phenomena can be interpreted as consequences of the absence of these symmetries.

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 $F_2 \wedge H_3$ 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. 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.