Supersymmetric $SU(5)\times U(1{)}_{\chi }$ and the Weak Gravity Conjecture

Abstract

The gauge symmetry $SU(5)\times U(1{)}_{\chi }$ is the unique maximal subgroup of SO(10) which retains manifest unification at $M_{GUT}$ of the Standard Model gauge couplings, especially if low scale supersymmetry is present. The spontaneous breaking of $U(1{)}_{\chi }$ at some intermediate scale leaves unbroken a $Z_2$ symmetry which is precisely `matter' parity. This yields a stable supersymmetric dark matter particle as well as topologically stable cosmic strings. Motivated by the weak gravity conjecture we impose unification of $SU(5)$ and $U(1{)}_{\chi }$ at an ultraviolet cutoff $\Lambda \sim {\alpha }_{\Lambda }^{1/2}{M}_P\approx 5\times 10^{17}$ GeV, where ${\alpha }_{\Lambda }$ denotes the $SU(5)$ gauge coupling at $\Lambda$ and $M_P\approx 2.4\times 10^{18}$ GeV is the reduced Planck Scale. The impact of dimension five operators suppressed by $\Lambda$ on gauge coupling unification, proton lifetime estimates and $b-\tau$ Yukawa unification is discussed. In particular, the gauge boson mediated proton decay into $e^{+}{\pi }^0$ can lie within the $2-\sigma$ sensitivity of HyperKamiokande. We also discuss how the intermediate scale strings may survive inflation while the $SU(5)$ monopoles are inflated away. The unbroken $Z_2$ symmetry provides an intriguing link between dark matter, black holes carrying `quantum hair' and cosmic strings.

arXiv comment6 pages, 6 figures

References in corpus (22)

• The String Landscape, Black Holes and Gravity as the Weakest Force
• The Top Quark Mass in Supersymmetric SO(10) Unification
• Large Scale Structure and Supersymmetric Inflation without Fine Tuning
• Black Holes and Large N Species Solution to the Hierarchy Problem
• Planck 2013 results. XXV. Searches for cosmic strings and other topological defects
• Black Hole Bound on the Number of Species and Quantum Gravity at LHC
• Letter of Intent: The Hyper-Kamiokande Experiment --- Detector Design and Physics Potential ---
• Search for Proton Decay via $p\to e^{+}{\pi }^0$ and $p\to {\mu }^{+}{\pi }^0$ in 0.31 megaton$\cdot$years exposure of the Super-Kamiokande Water Cherenkov Detector
• Inflation and Monopoles in Supersymmetric SU(4)_c x SU(2)_L x SU(2)_R
• Supersymmetric Hybrid Inflation with Non-Minimal Kahler potential
• Signals of Inflationary Models with Cosmic Strings
• Supersymmetric Hybrid Inflation Redux
• Grand unification and enhanced quantum gravitational effects
• Hybrid Inflation in the Complex Plane
• Update on Minimal Supersymmetric Hybrid Inflation in Light of PLANCK
• Inflation in Supersymmetric SU(5)
• Inflection-point inflation in hyper-charge oriented U(1)${}_X$ model
• SU(5)$\times$U(1)${}_X$ grand unification with minimal seesaw and $Z^{\prime }$-portal dark matter
• Yukawa Unification and the Superpartner Mass Scale
• Operator Analysis for Proton Decay in SUSY SO(10) GUT Models
• $b-\tau$ Yukawa Unification in SUSY SU(5) with Mirage Mediation: LHC and Dark Matter Implications
• Gravitational Corrections to Fermion Masses in Grand Unified Theories

Cited by in corpus (4)

• Festina Lente: EFT Constraints from Charged Black Hole Evaporation in de Sitter
• Exploring primordial black holes and gravitational waves with R-symmetric GUT Higgs inflation
• Radiative Symmetry breaking, Cosmic Strings and Observable Gravity Waves in $U(1{)}_R$ symmetric $SU(5)\times U(1{)}_{\chi }$
• Smooth Hybrid Inflation with Low Reheat Temperature and Observable Gravity Waves in $SU(5)\times U(1{)}_{\chi }$ Super-GUT