[Paper Review] Trends in Grand Unification: unification at strong coupling and composite models

V. A. Rubakov, S. Troitsky|ArXiv.org|Jan 20, 2000

advanced mathematical theories5 references3 citations

TL;DR

This paper proposes a novel approach to Grand Unification by exploring strongly coupled Grand Unified Theories (GUTs) where the Standard Model emerges as a low-energy effective theory of composite particles. Using a dual description inspired by Seiberg duality in SQCD, the authors construct a realistic model in which unification occurs at strong coupling, dynamically breaking supersymmetry and avoiding the need for a hidden sector, while preserving gauge coupling unification and solving the doublet-triplet splitting problem.

ABSTRACT

We review several problems of conventional Grand Unification and some new approaches. In particular, we discuss strongly coupled Grand Unified Theories. Standard Model may emerge as a low energy effective theory of composite particles in these models. We construct a realistic model of this kind.

Motivation & Objective

• To address the limitations of conventional Grand Unified Theories (GUTs), including the doublet-triplet splitting problem and the need for a hidden sector in supersymmetry breaking.
• To explore whether gauge coupling unification can be preserved in the absence of the Grand Desert, particularly when new states exist between the SUSY and GUT scales.
• To construct a realistic model in which the Standard Model arises as a low-energy effective theory of composite particles in a strongly coupled GUT.
• To investigate whether dynamical supersymmetry breaking can occur at the GUT scale without introducing a separate hidden sector.
• To demonstrate that strong coupling and composite dynamics can resolve key issues in conventional GUT scenarios, such as proton decay rate and coupling unification.

Proposed method

• Adopting a dual description inspired by Seiberg duality in SQCD, the model treats the MSSM with vector-like matter as a dual theory of a strongly coupled GUT.
• Using the one-loop renormalization group equations, the paper analyzes how beta functions change with additional vector-like matter, leading to strong coupling at high energies.
• The model employs a non-renormalizable superpotential $ W = m\,{\rm Tr}\Phi^{2} - \frac{1}{M}{\rm Tr}\Phi^{4} $ to break symmetry from SO(10) to $ SU(3)\times SU(2)\times U(1)\times U(1)' $.
• The vacuum expectation value of the adjoint field $ \Phi $ is set to $ B^\Phi = \sqrt{2mM/3}\,{\rm diag}(1,1,1,-1,-1) $, leading to the desired low-energy gauge group.
• The paper uses Dynkin diagram reduction to classify possible symmetry breaking patterns from SO(10), showing that removing two nodes via a non-renormalizable superpotential leads to the Standard Model gauge group plus an additional U(1) factor.
• The approach avoids fundamental superpotential terms and relies on strong dynamics to generate the correct low-energy spectrum and interactions.

Experimental results

Research questions

• RQ1 Can gauge coupling unification be preserved in the absence of the Grand Desert, even when new matter states exist between the SUSY and GUT scales?
• RQ2 Can a strongly coupled GUT dynamically break supersymmetry at the GUT scale without requiring a separate hidden sector?
• RQ3 Is it possible to construct a realistic model where the Standard Model emerges as a low-energy effective theory of composite particles in a strongly coupled GUT framework?
• RQ4 How can the doublet-triplet splitting problem be solved in a strongly coupled GUT without fine-tuning?
• RQ5 What are the implications of strong coupling for the unification scale and proton decay rate in composite GUT models?

Key findings

• The model realizes unification at strong coupling, where the MSSM with vector-like matter is dual to a strongly coupled GUT, avoiding the need for a hidden sector for SUSY breaking.
• The doublet-triplet splitting problem is naturally solved because the Higgs doublets and triplets arise from different representations in the composite dynamics, eliminating the need for fine-tuning.
• The unification scale is lowered due to strong coupling, and the theory remains consistent with proton decay constraints, as the triplet Higgs partners are not superheavy but dynamically suppressed.
• The inclusion of vector-like matter reduces the beta function coefficients, leading to loss of asymptotic freedom and signaling the onset of strong dynamics at high energies.
• The non-renormalizable superpotential $ W = m{\rm Tr}\Phi^{2} - \frac{1}{M}{\rm Tr}\Phi^{4} $ generates a vacuum with $ A^\Phi = 0 $, $ B^\Phi = \sqrt{2mM/3}\,{\rm diag}(1,1,1,-1,-1) $, breaking SO(10) to $ SU(3)\times SU(2)\times U(1)\times U(1)' $.
• The model avoids the need for a Grand Desert, as new physics (axions, see-saw scale, messengers) can be naturally embedded in the strongly coupled sector, resolving the hierarchy of scales.