Grand unification and the Planck scale: An $SO(10)$ example of radiative symmetry breaking

Abstract

Grand unification of gauge couplings and fermionic representations remains an appealing proposal to explain the seemingly coincidental structure of the Standard Model. However, to realise the Standard Model at low energies, the unified symmetry group has to be partially broken by a suitable scalar potential in just the right way. The scalar potential contains several couplings, whose values dictate the residual symmetry at a global minimum. Some (and possibly many) of the corresponding symmetry-breaking patterns are incompatible with the Standard Model and therefore non-admissible. Here, we initiate a systematic study of radiative symmetry breaking to thereby constrain viable initial conditions for the scalar couplings, for instance, at the Planck scale. We combine these new constraints on an admissible scalar potential with well-known constraints in the gauge-Yukawa sector into a general blueprint that carves out the viable effective-field-theory parameter space of any underlying theory of quantum gravity. We exemplify the constraining power of our blueprint within a non-supersymmetric $SO(10)$ GUT containing a ${16}_H$- and a ${45}_H$-dimensional scalar representation. We explicitly demonstrate that the requirement of successful radiative symmetry breaking to the correct subgroups significantly constraints the underlying microscopic dynamics. The presence of non-admissible radiative minima can even entirely exclude specific breaking chains: In the $SO(10)$ example, Pati-Salam breaking chains cannot be realised since the respective minima are never the deepest ones.

35 pages + appendix; 5 figures

References in corpus (44)

• The nonperturbative functional renormalization group and its applications
• Asymptotic safety guaranteed
• Top mass from asymptotic safety
• Search of scaling solutions in scalar-tensor gravity
• Fermion Masses in SO(10) Models
• Gauge Dependence of Gravitational Correction to Running of Gauge Couplings
• Quantum gravity and Standard-Model-like fermions
• Absence of gravitational contributions to the running Yang-Mills coupling
• Quantum gravity and charge renormalization
• Softened Gravity and the Extension of the Standard Model up to Infinite Energy
• Yukawa Sector of Minimal SO(10) Unification
• PyR@TE 3
• GroupMath: A Mathematica package for group theory calculations
• Constraining power of asymptotic safety for scalar fields
• Higgs Mass Bounds from Renormalization Flow for a Higgs-top-bottom model
• Safety in darkness: Higgs portal to simple Yukawa systems
• Stable Asymptotically Free Extensions (SAFEs) of the Standard Model
• Impact of generalized Yukawa interactions on the lower Higgs mass bound
• Scalegenesis and fermionic dark matters in the flatland scenario
• Fits to Non-Supersymmetric SO(10) Models with Type I and II Seesaw Mechanisms Using Renormalization Group Evolution
• Framework for an asymptotically safe Standard Model via dynamical breaking
• The weak-gravity bound in asymptotically safe gravity-gauge systems
• Quantum gravity, gauge coupling constants, and the cosmological constant
• Stability of domain walls in models with asymmetric potentials
• Analytical relations for the bound state spectrum of gauge theories with a Brout-Englert-Higgs mechanism
• Asymptotically free scaling solutions in nonabelian Higgs models
• Functional Renormalization and $\overline{\text{MS}}$
• Multi-scale Renormalization Group Methods for Effective Potentials with Multiple Scalar Fields
• Nonvanishing gravitational contribution to matter beta functions for vanishing dimensionful regulators
• Scaling relations and multicritical phenomena from Functional Renormalization
• A complete asymptotically safe embedding of the Standard Model
• General RGEs for dimensionful couplings in the $\overline{\mathrm{MS}}$ scheme
• Realizing unification in two different SO(10) models with one intermediate breaking scale
• Status update: asymptotically safe gravity-matter systems
• Grand unification and the Planck scale: An $SO(10)$ example of radiative symmetry breaking
• Quantum nature of the minimal potentially realistic $\mathrm{SO}(10)$ Higgs model
• Minima of Classically Scale-Invariant Potentials
• Gravitational corrections to two-loop beta function in quantum electrodynamics
• Allowed and observable phases in two-Higgs-doublet Standard Models
• Renormalization group improvement of the effective potential in six dimensions
• Light Higgs boson from multi-phase criticality in dynamical symmetry breaking
• Generalized Vanishing Theorems for Yukawa Couplings in Heterotic Compactifications
• Criticality of the $O(2)$ model with cubic anisotropies from nonperturbative renormalization
• Symmetry allowed, but unobservable, phases in renormalizable Gauge Field Theory Models

Cited by in corpus (7)

• From quantum gravity to gravitational waves through cosmic strings
• Grand unification and the Planck scale: An $SO(10)$ example of radiative symmetry breaking
• Shift-symmetric Horndeski gravity in the asymptotic-safety paradigm
• Stabilizing dark matter with quantum scale symmetry
• Electroweak phase transition with radiative symmetry breaking in Type-II seesaw with inert doublet
• Improved effective potential of Gildener-Weinberg models
• Grand Unified Origin of Enhanced Scalar Couplings: Connecting Radiative Electroweak Symmetry Breaking to SO(10) Dynamics