Anomaly and Cobordism Constraints Beyond Grand Unification: Energy Hierarchy

Abstract

A recent work [2006.16996] suggests that a 4d nonperturbative global anomaly of mod 16 class hinting a possible new hidden gapped topological sector beyond the Standard Model (SM) and Georgi-Glashow $su(5)$ Grand Unified Theory (GUT) with 15n chiral Weyl fermions and a discrete ${\mathbb{Z}}_{4,X}$ symmetry of $X=5(\mathbf{B}-\mathbf{L})-4Y$. This ${\mathbb{Z}}_{16}$ class global anomaly is a mixed gauge-gravitational anomaly between the discrete $X$ and spacetime backgrounds. The new topological sector has a GUT scale high energy gap, below its low energy encodes either a 4d noninvertible topological quantum field theory (TQFT), or a 5d short-range entangled invertible TQFT, or their combinations. This hidden topological sector provides the 't Hooft anomaly matching of the missing sterile right-handed neutrinos (3 generations of 16th Weyl fermions), and possibly also accounts for the Dark Matter sector. In the SM and $su(5)$ GUT, the discrete $X$ can be either a global symmetry or gauged. In the $so(10)$ GUT, the $X$ must become gauged, the 5d TQFT becomes noninvertible and long-range entangled (which can couple to dynamical gravity). In this work, we further examine the anomaly and cobordism constraints at higher energy scales above the $su(5)$ GUT to $so(10)$ GUT and $so(18)$ GUT (with Spin(10) and Spin(18) gauge groups precisely). We also find [2006.16996]'s proposal on new hidden gapped topological sectors can be consistent with anomaly matching under the energy/mass hierarchy. Novel ingredients along tuning the energy include various energy scales of anomaly-free symmetric mass generation (i.e., Kitaev-Wen mechanism), the Topological Mass/Energy Gap from anomalous symmetric topological order (attachable to a 5d ${\mathbb{Z}}_{4,X}$-symmetric topological superconductor), possible topological quantum phase transitions, and Ultra Unification that includes GUT with new topological sectors.

50 pages. Primers: arXiv:2006.16996, arXiv:1910.14668, arXiv:1810.00844, arXiv:1809.11171

References in corpus (7)

• Generalized Global Symmetries
• 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
• Line Operators in the Standard Model
• Interacting Topological Insulator and Emergent Grand Unified Theory
• Anomaly Obstructions to Symmetry Preserving Gapped Phases
• Interaction effects on 3D topological superconductors: surface topological order from vortex condensation, the 16 fold way and fermionic Kramers doublets

Cited by in corpus (8)

• Symmetric Mass Generation
• 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
• Deconfined Quantum Criticality among Grand Unified Theories