Chern-Weil global symmetries and how quantum gravity avoids them

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($$ {F}_2^2 $$ 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.

Compactness of brane moduli and the String Lamppost Principle in d > 6

“…Finally, we also note that the connectedness of the moduli space for the small instanton limit of every possible non-Abelian gauge group with eight supercharges is deeply connected with the fact that they all carry the same physical brane charge. As discussed in [22], this is related to demanding absence of Chern-Weil global symmetries.…”

Modular curves and the refined distance conjecture

“…Naively, this would suggest that the values of N that appear for K3 fibered CY threefolds are at most those that lead JHEP12(2021)088 to genus zero curves X 0 (N ) + . 13 The main problem with such an argument seems to be that non-trivial one-cycles in the weak coupling slice of moduli space that we are looking at might trivialize in the strong coupling region. Additionally, an explicit check would necessarily go beyond the Grassmannian constructions considered in this work, since the genus zero property only starts to fail starting from N = 20.…”

“…As of now, what are the most fundamental constraints on effective field theories that imply consistent coupling to quantum gravity is still under debate. Abstract principles like the absence of global symmetries [7][8][9][10][11][12][13] and topological operators [14,15], completeness of the spectrum [16], or the cobordism conjecture [17] seem very promising and have been used to argue for string universality in supersymmetric theories with a large number of uncompactified spacetime dimensions [18][19][20][21].…”

The Weak Gravity Conjecture: A Review

“…As a final direction for future research, let us remark that the statement of the WGC in the presence of Chern-Simons terms is, at present, not well understood. The recent work [137] presented an example of WGC mixing, in which the WGC for different p-form gauge fields are mixed up in the presence of Chern-Simons terms (see also [64,298,299,141]). These Chern-Simons terms imply that the gauge symmetry acquires a higher-group structure [300,301], and it seems likely that the full statement of the WGC is modified in the presence of such higher-group symmetries, reminiscent of how the WGC is modified to the Convex Hull Condition in theories with multiple U (1)s. Understanding this better might have interesting implications for axion monodromy.…”