2020/09/30 by Erich Poppitz, F. David Wandler
Physics and Astronomy · #Abelian group #Anomaly (physics) #Dirac fermion #Fermion #Gauge theory #Homogeneous space #Limit (mathematics) #Mixed anomaly #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #Quantum and Classical Electrodynamics #Symmetry (geometry) #Topological quantum field theory #hep-lat #hep-th
paper · pdf · doi:10.1007/jhep01(2021)091
70 pages, 9 figures. Version to appear in JHEP. Typos fixed, references added
openalex created_date 2020/10/08 · arxiv created 2020/12/16 · openalex publication_date 2021/01/18 · arxiv updated 2021/02/03 · openalex updated_date 2026/08/05
A bstract We explicitly calculate the topological terms that arise in IR effective field theories for SU( N ) gauge theories on ℝ 3 × 𝕊 1 by integrating out all but the lightest modes. We then show how these terms match all global-symmetry ’t Hooft anomalies of the UV description. We limit our discussion to theories with abelian 0-form symmetries, namely those with one flavour of adjoint Weyl fermion and one or zero flavours of Dirac fermions. While anomaly matching holds as required, it takes a different form than previously thought. For example, cubic- and mixed-U(1) anomalies are matched by local background-field-dependent topological terms (background TQFTs) instead of chirallagrangian Wess-Zumino terms. We also describe the coupling of 0-form and 1-form symmetry backgrounds in the magnetic dual of super-Yang-Mills theory in a novel way, valid throughout the RG flow and consistent with the monopole-instanton ’t Hooft vertices. We use it to discuss the matching of the mixed chiral-center anomaly in the magnetic dual.