[Paper Review] Proceedings to the 9th Workshop 'What Comes Beyond the Standard Models', Bled, September 16. - 26., 2006, Slovenia

Stefano Ansoldi, D. L. Bennett+10 more|ArXiv.org|Dec 20, 2006

International Science and Diplomacy58 references15 citations

TL;DR

This paper proposes a conjecture that dimensional reduction of a gauge theory with one or more compactified dimensions leads to an effective lower-dimensional theory exhibiting a first-order phase transition, where the original couplings naturally tune to the critical line—a phenomenon interpreted as a dynamical mechanism for coupling self-tuning. The key result is that this transition, while unphysical in the full theory, may provide a dynamical origin for the Multiple Point Principle, suggesting that the observed values of couplings in nature could be selected by such compactification-induced phase transitions.

ABSTRACT

Contents: 1. Child Universes in the Laboratory (S. Ansoldi and E.I. Guendelman) 2. Relation between Finestructure Constants at the Planck Scale from Multiple Point Principle (D.L. Bennett, L.V. Laperashvili and H.B. Nielsen) 3. On the Origin of Families of Fermions and Their Mass Matrices -- Approximate Analyses of Properties of Four Families Within Approach Unifying Spins and Charges (M. Breskvar, D. Lukman and N.S. Mankoc Borstnik) 4. Cosmoparticle Physics: Cross-disciplinary Study of Physics Beyond the Standard Model (M.Yu. Khlopov) 5. Discussion Section on 4th Generation (M.Yu. Khlopov) 6. Involution Requirement on a Boundary Makes Massless Fermions Compactified on a Finite Flat Disk Mass Protected (N.S. Mankoc Borstnik and H.B. Nielsen) 7. How Can Group Theory be Generalized so Perhaps Providing Further Information About Our Universe? (R. Mirman) 8. FutureDependent Initial Conditions from Imaginary Part in Lagrangian (H.B. Nielsen and M. Ninomiya) 9. Coupling Self-tuning to Critical Lines From Highly Compact Extra Dimensions (K. Petrov)

Motivation & Objective

• To investigate whether dimensional reduction of a higher-dimensional gauge theory can lead to an effective lower-dimensional theory with emergent phase transitions.
• To explore whether the critical behavior of such a reduced theory could explain the observed fine-tuning of coupling constants in the Standard Model.
• To examine if the observed values of couplings in nature might be dynamically selected by a phase transition arising from compactified dimensions.
• To test the conjecture that the couplings of the original theory are naturally tuned to the critical line of the effective theory’s phase diagram.
• To assess whether such a mechanism could provide a physical basis for the Multiple Point Principle without requiring fine-tuning.

Proposed method

• Perform a perturbative dimensional reduction of a D-dimensional gauge theory with one or more compact dimensions, focusing on the temporal direction.
• Fix gauge degrees of freedom using a static, time-averaged Landau gauge condition to isolate physical degrees of freedom.
• Introduce a scalar field φ(x) derived from the compactified gauge component A₀(x), transforming the effective action into a (D−1)-dimensional theory.
• Construct the effective action S_eff as a sum of three parts: a pure gauge term S_W², a gauge-covariant kinetic term S_U,φ, and a self-interaction term S_φ (Higgs-like potential).
• Express the couplings h₂ and h₄ in the effective Higgs potential in terms of the original theory’s parameters g₀ and L₀.
• Analyze the effective theory non-perturbatively to identify phase transitions, particularly a first-order transition driven by φ → −φ symmetry.

Experimental results

Research questions

• RQ1 Can a higher-dimensional gauge theory with compactified dimensions give rise to an effective lower-dimensional theory with a first-order phase transition?
• RQ2 Why do the couplings of the original theory appear to lie precisely on the critical line of the effective theory’s phase transition?
• RQ3 Is the observed self-tuning of couplings in the effective theory a consequence of the compactification process, rather than fine-tuning?
• RQ4 Can this mechanism provide a dynamical explanation for the Multiple Point Principle?
• RQ5 What is the role of non-perturbative effects in the emergence of critical behavior in the reduced theory?

Key findings

• The effective (D−1)-dimensional theory exhibits a first-order phase transition, with spontaneous breaking of the φ → −φ symmetry, indicating a critical line in coupling space.
• The original couplings g₀ and L₀ are found to lie precisely on the critical line of the effective theory’s phase diagram, suggesting a dynamical tuning mechanism.
• This self-tuning occurs despite the absence of fine-tuning in the original theory, indicating that the criticality is a consequence of the compactification and dimensional reduction process.
• The phase transition is unphysical in the full D-dimensional theory but emerges as a feature of the effective description, implying that the critical couplings are not accidental.
• The mechanism is supported by numerical and analytical results in 3D (SU(3)) and 4D (SU(2)) models, suggesting potential universality across dimensions.
• The presence of multiple compact dimensions may lead to multi-critical points, potentially offering a framework for the Multiple Point Principle as an emergent property of compactification.