2019/10/31 by Zheyan Wan, Juven Wang · 1 citation
Physics and Astronomy · Mathematics · #hep-th #cond-mat.str-el #hep-lat #hep-ph #math.AT
paper · pdf · doi:10.1007/jhep07(2020)062
published as JHEP 07 062 (2020) · 91 pages. v4: Refinement and Refs added. More clarifications with new subsections and appendices on the same cobordism group results. Part of the work is reported in Workshop on Lattice for Beyond the Standard Model physics on May 2-3, 2019 at Syracuse University
arxiv created 2020/06/05 · arxiv updated 2021/01/29
We classify and characterize all invertible anomalies and all allowed topological terms related to various Standard Models (SM), Grand Unified Theories (GUT), and Beyond Standard Model (BSM) physics. By all anomalies, we mean the inclusion of (1) perturbative/local anomalies captured by perturbative Feynman diagram loop calculations, classified by ℤ free classes, and (2) non-perturbative/global anomalies, classified by finite group ℤN torsion classes. Our work built from [arXiv:1812.11967] fuses the math tools of Adams spectral sequence, Thom-Madsen-Tillmann spectra, and Freed-Hopkins theorem. For example, we compute bordism groups ΩGd and their invertible topological field theory invariants, which characterize dd topological terms and (d-1)d anomalies, protected by the following symmetry group G: Spin× (SU(3)× SU(2)× U(1))/(ℤq) for SM with q=1,2,3,6; (Spin × Spin(n))/(ℤ2F) or Spin × Spin(n) for SO(10) or SO(18) GUT as n=10, 18; Spin × SU(n) for Georgi-Glashow SU(5) GUT as n=5; \fracSpin× \fracSU(4)×(SU(2)× SU(2))ℤq'ℤ2F for Pati-Salam GUT as q'=1,2; and others. For SM with an extra discrete symmetry, we obtain new anomaly matching conditions of ℤ16, ℤ4, and ℤ2 classes in 4d beyond the familiar Witten anomaly. Our approach offers an alternative view of all anomaly matching conditions built from the lower-energy (B)SM or GUT, in contrast to high-energy Quantum Gravity or String Theory Landscape v.s. Swampland program, as bottom-up/top-down complements. Symmetries and anomalies provide constraints of kinematics, we further suggest constraints of quantum gauge dynamics, and new predictions of possible extended defects/excitations plus hidden BSM non-perturbative topological sectors.