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| Format: | Recurso digital |
| Language: | English |
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Zenodo
2025
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| Online Access: | https://doi.org/10.5281/zenodo.17188551 |
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Table of Contents:
- <p>Σ-Topological Theory of Emergence (Σ-TTE) v3.0: Complete Microscopic Theory from M-Theory with Explicit FRG Formalism</p> <p>Author: Alexander Bolikov<br>Version: 3.0 (mathematically rigorous formulation)<br>Date: September 24, 2024</p> <p>Abstract:</p> <p>We present a complete microscopic formulation of Σ-Topological Theory of Emergence (Σ-TTE) as a consistent compactification of M-theory on G2-holonomy manifolds. Σ-defects are identified with associative cycles, whose topology determines the gauge groups of the Standard Model through the Horava-Witten mechanism. We develop a rigorous Functional Renormalization Group (FRG) formalism with explicit stochastic averaging over topological defect configurations, enabling the derivation of:</p> <p>- Induced gravity from the mass spectrum of vacuum fluctuations<br>- The arrow of time from monotonic growth of vacuum relaxation entropy <br>- The hierarchy of fermion masses and mixing matrices from intersection geometry of cycles<br>- The cosmological constant relaxation mechanism</p> <p>The theory provides a complete set of testable predictions for modern experiments.</p> <p>Key Features:</p> <p>1. MICROSCOPIC FOUNDATION: Based on M-theory compactified on 7-dimensional G2-holonomy manifolds, with associative cycles serving as topological defects (Σ-defects)</p> <p>2. STANDARD MODEL EMERGENCE: Gauge groups SU(3)C × SU(2)L × U(1)Y arise from G2 singularities via Horava-Witten mechanism</p> <p>3. RIGOROUS FRG FORMALISM: Extended effective average action incorporating topological defect fields with explicit β-functions for gravitational, Yukawa, and topological sectors</p> <p>4. BOLIKOV GLASS: Critical phase description using order parameter τ(x) satisfying generalized Lipatov-Faddeev equation with fractal dimension Deff = 2.62 ± 0.03</p> <p>5. INDUCED GRAVITY: Effective gravitational action derived from vacuum fluctuation spectrum with scale-dependent Newton constant and cosmological term</p> <p>6. ARROW OF TIME: Derived from monotonic growth of vacuum relaxation entropy connected to universe expansion</p> <p>7. MASS HIERARCHY: Fermion masses and mixing matrices determined by intersection volumes of associative cycles in extra dimensions</p> <p>Theoretical Predictions:</p> <p>- Fractal dimension: Deff = 2.62 ± 0.03 (testable with Euclid, LSST)<br>- Tensor-to-scalar ratio: r = 0.010 ± 0.001 (LiteBIRD, CMB-S4) <br>- Sum of neutrino masses: Σmν = 0.12 ± 0.02 eV (KATRIN, DUNE)<br>- 21-cm line spectral tilt: α = -2.48 ± 0.04 (SKA)<br>- Gravitational wave phase distortions: 0.05-0.3%</p> <p>Methodology:</p> <p>The theory combines mathematical physics approaches including:<br>- Differential geometry of G2 manifolds<br>- Topological defect theory<br>- Functional Renormalization Group methods<br>- Stochastic field theory<br>- String theory compactifications<br>- Critical phenomena analysis</p> <p>Code Availability:</p> <p>Python implementation for numerical solution of FRG equations provided in Appendix B, enabling reproduction of hierarchy parameter εd ≈ 0.15 and other quantitative predictions.</p> <p>Significance:</p> <p>Σ-TTE v3.0 represents a comprehensive framework unifying quantum gravity, particle physics, and cosmology through topological emergence principles, with all parameters derived from first principles and testable predictions for next-generation experiments.</p> <p>Keywords: Quantum gravity, M-theory, G2-holonomy, topological defects, functional renormalization group, emergent gravity, arrow of time, mass hierarchy, cosmological constant, fractal cosmology, string phenomenology</p>