2022/06/30 by T. Daniel Brennan, Brennan, T. Daniel, Clay Córdova +4 · 5 citations
Mathematics · Physics and Astronomy · #Anomaly (physics) #Black Holes and Theoretical Physics #Context (archaeology) #Fermion #Fractionalization #Gauge anomaly #Gauge group #Gauge symmetry #Gauge theory #Geometry #Homogeneous space #Law #Mathematical physics #Mathematics #Mixed anomaly #Physics #Physics of Superconductivity and Magnetism #Pulsars and Gravitational Waves Research #Quantum mechanics #Supersymmetric gauge theory #Symmetry (geometry) #Theoretical physics
paper · pdf · doi:10.48550/arxiv.2206.15401
openalex publication_date 2022/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We explore the connection between the global symmetry quantum numbers of line defects and 't Hooft anomalies. Relative to local (point) operators, line defects may transform projectively under both internal and spacetime symmetries. This phenomenon is known as symmetry fractionalization, and in general it signals the presence of certain discrete 't Hooft anomalies. We describe this in detail in the context of free Maxwell theory in four dimensions. This understanding allows us to deduce the 't Hooft anomalies of non-Abelian gauge theories with renormalization group flows into Maxwell theory by analyzing the fractional quantum numbers of dynamical magnetic monopoles. We illustrate this method in SU(2) gauge theories with matter fermions in diverse representations of the gauge group. For adjoint matter, we uncover a mixed anomaly involving the 0-form and 1-form symmetries, extending previous results. For SU(2) QCD with fundamental fermions, the 't Hooft anomaly for the 0-form symmetries that is encoded by the fractionalization patterns of lines in the Maxwell phase is a consequence of the familiar perturbative (triangle) anomaly.