Anomaly and Cobordism Constraints Beyond the Standard Model: Topological Force

Abstract

Standard lore uses local anomalies to check the kinematic consistency of gauge theories coupled to chiral fermions, e.g. Standard Models (SM). Based on a systematic cobordism classification, we examine constraints from invertible quantum anomalies (including all perturbative local and nonperturbative global anomalies) for gauge theories. We also clarify the different uses of these anomalies: including (1) anomaly cancellations of dynamical gauge fields, (2) 't Hooft anomaly matching conditions of background fields of global symmetries, and others. We apply several 4d ${\mathbb{Z}}_n$ anomaly constraints of $n=16,4,2$ classes, beyond the familiar Feynman-graph perturbative $\mathbb{Z}$ class local anomalies. As an application, for (SU(3)$\times$SU(2)$\times$U(1))/${\mathbb{Z}}_q$ SM (with $q=1,2,3,6$) and SU(5) Grand Unification with 15n chiral Weyl fermions and with a discrete baryon minus lepton number $X=5(\mathbf{B}-\mathbf{L})-4Y$ preserved, we discover a new hidden gapped sector previously unknown to the SM and Georgi-Glashow model. The gapped sector at low energy contains either (1) 4d non-invertible topological quantum field theory (TQFT, above the energy gap with heavy fractionalized anyon excitations from 1d particle worldline and 2d string worldsheet, inaccessible directly from Dirac or Majorana mass gap of the 16th Weyl fermions [i.e., right-handed neutrinos], but accessible via a topological quantum phase transition), or (2) 5d invertible TQFT in extra dimensions. Above a higher energy scale, the discrete $X$ becomes dynamically gauged, the entangled Universe in 4d and 5d is mediated by Topological Force. Our model potentially resolves puzzles, surmounting sterile neutrinos and dark matter, in fundamental physics.

arXiv comment68 pages. Sequel: arXiv:2008.06499, arXiv:1910.14668. Primers: arXiv:1812.11967, arXiv:1711.11587, arXiv:1705.06728, arXiv:1612.09298. v2: Significant revision. Correct statements on 4d TQFTs in Sec 5. We focus only on the even class such as a 2 mod 16 symmetric anomalous 4d TQFT. We can also introduce 5d invertible TQFTs and right-hand neutrinos

References in corpus (66)

• Topological Insulators
• Topological insulators and superconductors
• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Classification of topological insulators and superconductors in three spatial dimensions
• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• Generalized Global Symmetries
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Symmetries and Strings in Field Theory and Gravity
• Zoo of quantum-topological phases of matter
• Topological phases of fermions in one dimension
• Lieb-Schultz-Mattis in Higher Dimensions
• Symmetry Protected Topological phases of Quantum Matter
• The effects of interactions on the topological classification of free fermion systems
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Theta, Time Reversal, and Temperature
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Fermion Path Integrals And Topological Phases
• Fermionic Symmetry Protected Topological Phases and Cobordisms
• On gauging finite subgroups
• Interacting fermionic topological insulators/superconductors in three dimensions
• Classifying gauge anomalies through SPT orders and classifying gravitational anomalies through topological orders
• Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
• What is the Discrete Gauge Symmetry of the MSSM?
• Braiding statistics of loop excitations in three dimensions
• 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
• Dual Dirac liquid on the surface of the electron topological insulator
• Dai-Freed anomalies in particle physics
• Anomalies of discrete symmetries in three dimensions and group cohomology
• Non-Abelian String and Particle Braiding in Topological Order: Modular SL(3,Z) Representation and 3+1D Twisted Gauge Theory
• Symmetry protected topological phases in non-interacting fermion systems
• Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions
• Discrete Anomaly Matching
• Topological invariants for gauge theories and symmetry-protected topological phases
• Anomalies of discrete symmetries in various dimensions and group cohomology
• A New SU(2) Anomaly
• Developments in Topological Gravity
• Adjoint QCD${}_4$, Deconfined Critical Phenomena, Symmetry-Enriched Topological Quantum Field Theory, and Higher Symmetry-Extension
• Line Operators in the Standard Model
• Why are fractional charges of orientifolds compatible with Dirac quantization?
• An Adventure in Topological Phase Transitions in 3 + 1-D: Non-abelian Deconfined Quantum Criticalities and a Possible Duality
• Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms
• Two-flavor adjoint QCD
• Bosonic Anomalies, Induced Fractional Quantum Numbers and Degenerate Zero Modes: the anomalous edge physics of Symmetry-Protected Topological States
• Beyond Standard Models and Grand Unifications: Anomalies, Topological Terms, and Dynamical Constraints via Cobordisms
• Interacting Topological Insulator and Emergent Grand Unified Theory
• A lattice non-perturbative definition of an SO(10) chiral gauge theory and its induced standard model
• Anomaly Obstructions to Symmetry Preserving Gapped Phases
• Anomaly Constraints on Gapped Phases with Discrete Chiral Symmetry
• Anomaly indicators for time-reversal symmetric topological orders
• Candidate Phases for SU(2) Adjoint QCD${}_4$ with Two Flavors from $\mathcal{N}=2$ Supersymmetric Yang-Mills Theory
• Quantum 4d Yang-Mills Theory and Time-Reversal Symmetric 5d Higher-Gauge Topological Field Theory
• Interaction effects on 3D topological superconductors: surface topological order from vortex condensation, the 16 fold way and fermionic Kramers doublets
• A Solution to the 1+1D Gauged Chiral Fermion Problem
• Higher Anomalies, Higher Symmetries, and Cobordisms III: QCD Matter Phases Anew
• The Origin of Families and $SO(18)$ Grand Unification
• A categorification of the Jones polynomial
• Discrete gauge anomalies revisited
• Quantum Statistics and Spacetime Surgery
• Landau ordering phase transitions beyond the Landau paradigm
• Unwinding Short-Range Entanglement
• Interacting Topological Superconductors and possible Origin of $16n$ Chiral Fermions in the Standard Model
• (3+1)-TQFTs and Topological Insulators

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• Symmetric Mass Generation
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• Comments on Symmetric Mass Generation in 2d and 4d
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• Nonperturbative effects in the Standard Model with gauged 1-form symmetry
• Higher Anomalies, Higher Symmetries, and Cobordisms III: QCD Matter Phases Anew
• Gauge Enhanced Quantum Criticality Between Grand Unifications: Categorical Higher Symmetry Retraction
• Cobordism and Deformation Class of the Standard Model
• Ultra Unification
• Unwinding Fermionic SPT Phases: Supersymmetry Extension
• Gauge Enhanced Quantum Criticality Beyond the Standard Model
• Proton Stability: From the Standard Model to Beyond Grand Unification
• Fractionally Charged Particles at the Energy Frontier: The SM Gauge Group and One-Form Global Symmetry
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