2018/12/31 by Zheyan Wan, Juven Wang, Yunqin Zheng
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cobordism #Gauge (firearms) #Gauge theory #Generator (circuit theory) #Homotopy and Cohomology in Algebraic Topology #Manifold (fluid mechanics) #Noncommutative and Quantum Gravity Theories #Quantum field theory #Sigma model #Topological quantum field theory #Topology (electrical circuits) #cond-mat.str-el #hep-lat #hep-ph #hep-th #math.AT
paper · pdf · doi:10.1016/j.aop.2020.168074
published as Annals of Physics 414, 168074 (2020) · 46 pages, two columns. v5: Refinement, and correction to the anomalies at N = 4. v4: Sec IX provides the symmetry-extended TQFTs; while the symmetry-preserving TQFTs actually become spontaneously symmetry-breaking, agreed with Cordova-Ohmori's work. See companions arXiv:1812.11967 and arXiv:1904.00994
openalex created_date 2019/01/11 · arxiv created 2019/10/16 · openalex publication_date 2020/01/20 · arxiv updated 2020/02/10 · openalex updated_date 2026/08/06
We hypothesize a new and more complete set of anomalies of certain quantum field theories (QFTs) and then give an eclectic verification. First, we propose a set of 't Hooft higher anomalies of 4d time-reversal symmetric pure SU(N)-Yang-Mills (YM) gauge theory with a second-Chern-class topological term at θ=π, via 5d cobordism invariants (higher symmetry-protected topological states), with N = 2, 3, 4 and others. Second, we propose a set of 't Hooft anomalies of 2d \mathbbCPN-1-sigma models with a first-Chern-class topological term at θ=π, by enlisting all possible 3d cobordism invariants and selecting the matched terms. Based on algebraic/geometric topology, QFT analysis, manifold generator correspondence, condensed matter inputs such as stacking PSU(N)-generalized Haldane quantum spin chains, and additional physics criteria, we derive a correspondence between 5d and 3d new invariants. Thus we broadly prove a potentially complete anomaly-matching between 4d SU(N) YM and 2d \mathbbCPN-1 models at N = 2, and suggest new (but maybe incomplete) anomalies at N = 4. We formulate a higher-symmetry analog of "Lieb-Schultz-Mattis theorem" to constrain the low-energy dynamics.