Ultra Unification

Abstract

Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). In this work, we propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the baryon minus lepton number $\mathbf{B}-\mathbf{L}$, the electroweak hypercharge $Y$, and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary Lorentz invariant topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT, or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase). Alternatively, there could also be right-handed "sterile" neutrinos, gapless unparticle physics, more general interacting conformal field theories, or gravity with topological cobordism constraints, or their combinations to altogether cancel the mixed gauge-gravitational anomaly. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations) or gapless conformal matter. Physical characterizations of these gapped extended objects require the mathematical theories of cohomology, cobordism, or category. Although weaker than the weak force, Topological Force is infinite-range or long-range which does not decay in the distance, and mediates between the linked worldvolume trajectories via fractional or categorical statistical interactions.

38 pages. Sequel to: arXiv:1910.14668, arXiv:2006.16996, arXiv:2008.06499. Supplementary: arXiv:1809.11171, arXiv:1705.06728. Physical Review journal version accepted subtitle: Unified model beyond grand unification. v3: refinement, and more clarifications on math/physics and neutrino masses. Related talks: https://www.youtube.com/results?search_query=Ultra+Unification+Quantum+Criticality+Wang

References in corpus (15)

• Symmetries and Strings in Field Theory and Gravity
• Unparticle Physics
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Non-Abelian String and Particle Braiding in Topological Order: Modular SL(3,Z) Representation and 3+1D Twisted Gauge Theory
• Topological invariants for gauge theories and symmetry-protected topological phases
• Generalized modular transformations in 3+1D topologically ordered phases and triple linking invariant of loop braiding
• Line Operators in the Standard Model
• Interacting Topological Insulator and Emergent Grand Unified Theory
• Cobordism Classes and the Swampland
• Gauge Enhanced Quantum Criticality Between Grand Unifications: Categorical Higher Symmetry Retraction
• Cobordism and Deformation Class of the Standard Model
• Unwinding Fermionic SPT Phases: Supersymmetry Extension
• Gauge Enhanced Quantum Criticality and Time Reversal Domain Wall: SU(2) Yang-Mills Dynamics with Topological Terms
• Gauge Enhanced Quantum Criticality Beyond the Standard Model
• Anomaly and Cobordism Constraints Beyond Grand Unification: Energy Hierarchy

Cited by in corpus (9)

• Symmetric Mass Generation
• The anomaly that was not meant IIB
• Cobordism and Deformation Class of the Standard Model
• Categorical Symmetry of the Standard Model from Gravitational Anomaly
• Gauge Enhanced Quantum Criticality Beyond the Standard Model
• Proton Stability: From the Standard Model to Beyond Grand Unification
• CT or P Problem and Symmetric Gapped Fermion Solution
• Deconfined Quantum Criticality among Grand Unified Theories
• Boundary topological orders of (4+1)d fermionic ${\mathbb{Z}}_{2N}^{\mathrm{F}}$ SPT states