Beyond Standard Models and Grand Unifications: Anomalies, Topological Terms, and Dynamical Constraints via Cobordisms

Abstract

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 $\mathbb{Z}$ free classes, and (2) non-perturbative/global anomalies, classified by finite group ${\mathbb{Z}}_N$ 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 ${\Omega }_d^G$ and their invertible topological field theory invariants, which characterize $d$d topological terms and $(d-1)$d anomalies, protected by the following symmetry group $G$: $Spin\times \frac{SU(3)\times SU(2)\times U(1)}{{\mathbb{Z}}_q}$ for SM with $q=1,2,3,6$; $\frac{Spin\times Spin(n)}{{\mathbb{Z}}_2^F}$ or $Spin\times Spin(n)$ for SO(10) or SO(18) GUT as $n=10,18$; $Spin\times SU(n)$ for Georgi-Glashow SU(5) GUT as $n=5$; $\frac{Spin\times \frac{SU(4)\times (SU(2)\times SU(2))}{{\mathbb{Z}}_{q^{\prime }}}}{{\mathbb{Z}}_2^F}$ for Pati-Salam GUT as $q^{\prime }=1,2$; and others. For SM with an extra discrete symmetry, we obtain new anomaly matching conditions of ${\mathbb{Z}}_{16}$, ${\mathbb{Z}}_4$, and ${\mathbb{Z}}_2$ 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.

arXiv comment91 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

References in corpus (59)

• Topological Insulators
• Topological insulators and superconductors
• Topological Field Theory of Time-Reversal Invariant Insulators
• Periodic table for topological insulators and superconductors
• Generalized Global Symmetries
• The String Landscape, Black Holes and Gravity as the Weakest Force
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Symmetries and Strings in Field Theory and Gravity
• The Swampland: Introduction and Review
• Zoo of quantum-topological phases of matter
• Lieb-Schultz-Mattis in Higher Dimensions
• Symmetry Protected Topological phases of Quantum Matter
• Reading between the lines of four-dimensional gauge theories
• The String Landscape and the Swampland
• Theta, Time Reversal, and Temperature
• Fermion Path Integrals And Topological Phases
• Fermionic Symmetry Protected Topological Phases and Cobordisms
• Interacting fermionic topological insulators/superconductors in three dimensions
• Monopoles, Duality, and String Theory
• Classifying gauge anomalies through SPT orders and classifying gravitational anomalies through topological orders
• What is the Discrete Gauge Symmetry of the MSSM?
• The "Parity" Anomaly On An Unorientable Manifold
• Note on Discrete Gauge Anomalies
• Eta-Invariants and Determinant Lines
• Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology
• Field theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology and beyond
• Dai-Freed anomalies in particle physics
• Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions
• Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions
• Discrete Anomaly Matching
• A New SU(2) Anomaly
• Higher Anomalies, Higher Symmetries, and Cobordisms I: Classification of Higher-Symmetry-Protected Topological States and Their Boundary Fermionic/Bosonic Anomalies via a Generalized Cobordism Theory
• Adjoint QCD${}_4$, Deconfined Critical Phenomena, Symmetry-Enriched Topological Quantum Field Theory, and Higher Symmetry-Extension
• On the cobordism classification of symmetry protected topological phases
• Line Operators in the Standard Model
• Why are fractional charges of orientifolds compatible with Dirac quantization?
• Non-invertible anomalies and mapping-class-group transformation of anomalous partition functions
• Time Reversal, SU(N) Yang-Mills and Cobordisms: Interacting Topological Superconductors/Insulators and Quantum Spin Liquids in 3+1D
• Beyond Standard Models and Grand Unifications: Anomalies, Topological Terms, and Dynamical Constraints via Cobordisms
• Anomaly Obstructions to Symmetry Preserving Gapped Phases
• A lattice non-perturbative definition of an SO(10) chiral gauge theory and its induced standard model
• Cobordism Classes and the Swampland
• Quantum 4d Yang-Mills Theory and Time-Reversal Symmetric 5d Higher-Gauge Topological Field Theory
• A Solution to the 1+1D Gauged Chiral Fermion Problem
• A Non-Perturbative Definition of the Standard Models
• New Higher Anomalies, SU(N) Yang-Mills Gauge Theory and ${\mathbb{CP}}^{\mathrm{N}-1}$ Sigma Model
• Fermion masses without symmetry breaking in two spacetime dimensions
• Higher Anomalies, Higher Symmetries, and Cobordisms III: QCD Matter Phases Anew
• Line Operators of Gauge Theories on Non-Spin Manifolds
• Anomaly Inflow and the $\eta$-Invariant
• The Origin of Families and $SO(18)$ Grand Unification
• GSO projections via SPT phases
• Quantum Statistics and Spacetime Surgery
• Discrete gauge anomalies revisited
• Anomaly interplay in $U(2)$ gauge theories
• Anomaly and Cobordism Constraints Beyond the Standard Model: Topological Force
• Quantum Statistics and Spacetime Topology: Quantum Surgery Formulas
• Interacting Topological Superconductors and possible Origin of $16n$ Chiral Fermions in the Standard Model
• Homotopy Theoretic Classification of Symmetry Protected Phases

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• Beyond Standard Models and Grand Unifications: Anomalies, Topological Terms, and Dynamical Constraints via Cobordisms
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• On the consistency of a class of R-symmetry gauged 6D N=(1,0) supergravities
• The Smith Fiber Sequence and Invertible Field Theories
• Comments on the Atiyah-Patodi-Singer index theorem, domain wall, and Berry phase
• Embedding of the Georgi-Glashow $SU(5)$ model in the superconformal algebra
• Boundary topological orders of (4+1)d fermionic ${\mathbb{Z}}_{2N}^{\mathrm{F}}$ SPT states
• Boundary condition and reflection anomaly in $2+1$ dimensions
• Flavor Hierarchy from Smooth Confinement
• Integer solutions to the anomaly equations for a class of chiral gauge theories