Monopole Breaking of Chern-Weil Symmetries

Abstract

Gauge theories in $d$ dimensions with a nontrivial fundamental group admit a $(d-3)$-form magnetic symmetry and a $(d-5)$-form instantonic symmetry. These are examples of Chern-Weil symmetries, with conserved currents built out of the gauge field strength, which can only be explicitly broken through violations of the Bianchi identity. For U(1) gauge theory, it is clear that magnetic monopoles violate not only the $(d-3)$-form magnetic symmetry but also lower-form symmetries like the instantonic symmetry. It is also known that an improved instanton number symmetry current, which is conserved, can be constructed in the case that the magnetic monopole admits a dyonic excitation. We study the generalization to other gauge groups, showing that magnetic monopoles also violate instantonic symmetries for nonabelian groups like PSU($n$), and that dyon modes can restore such symmetries. Furthermore, we show that in many (but not all) examples where a gauge group $G$ is Higgsed to a gauge group $H$, the structure of monopoles and dyons emerging from the Higgsing process explicitly breaks the instantonic symmetries of $H$ to those of $G$. The meaning of explicit breaking of a $(d-5)$-form symmetry is clearest for $d>4$, but these results also extend to $d=4$, where the breaking is interpreted as an obstruction to coupling the theory to a background axion field.

49 pages, 3 figures; version accepted for publication in SciPost

References in corpus (15)

• Generalized Global Symmetries
• Symmetries and Strings in Field Theory and Gravity
• Instanton operators and symmetry enhancement in 5d supersymmetric gauge theories
• Lecture Notes on Generalized Symmetries and Applications
• An Introduction to Higher-Form Symmetries
• What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
• Cobordism Classes and the Swampland
• On completeness and generalized symmetries in quantum field theory
• Introduction to Generalized Global Symmetries in QFT and Particle Physics
• Instanton Operators in Five-Dimensional Gauge Theories
• Axion Mass from Magnetic Monopole Loops
• Field theories with higher-group symmetry from composite currents
• Gravitational Solitons and Completeness
• Extra-Dimensional Axion Expectations
• Lower-Form Symmetries