Weak Gravity Conjecture, Multiple Point Principle and the Standard Model Landscape

Abstract

The requirement for an ultraviolet completable theory to be well-behaved upon compactification has been suggested as a guiding principle for distinguishing the landscape from the swampland. Motivated by the weak gravity conjecture and the multiple point principle, we investigate the vacuum structure of the standard model compactified on $S^1$ and $T^2$. The measured value of the Higgs mass implies, in addition to the electroweak vacuum, the existence of a new vacuum where the Higgs field value is around the Planck scale. We explore two- and three-dimensional critical points of the moduli potential arising from compactifications of the electroweak vacuum as well as this high scale vacuum, in the presence of Majorana/Dirac neutrinos and/or axions. We point out potential sources of instability for these lower dimensional critical points in the standard model landscape. We also point out that a high scale $Ad{S}_4$ vacuum of the Standard Model, if exists, would be at odd with the conjecture that all non-supersymmetric $AdS$ vacua are unstable. We argue that, if we require a degeneracy between three- and four-dimensional vacua as suggested by the multiple point principle, the neutrinos are predicted to be Dirac, with the mass of the lightest neutrino O(1-10) meV, which may be tested by future CMB, large scale structure and $21$cm line observations.

56 pages, 22 figures, published version

References in corpus (45)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• The String Landscape, Black Holes and Gravity as the Weakest Force
• Quantization of Four-form Fluxes and Dynamical Neutralization of the Cosmological Constant
• Higgs mass and vacuum stability in the Standard Model at NNLO
• Investigating the near-criticality of the Higgs boson
• The String Landscape and the Swampland
• The DESI Experiment, a whitepaper for Snowmass 2013
• Reionization and the Cosmic Dawn with the Square Kilometre Array
• Wormholes, Emergent Gauge Fields, and the Weak Gravity Conjecture
• Naturalness and the Weak Gravity Conjecture
• Standard Model Criticality Prediction: Top mass 173 +/- 5 GeV and Higgs mass 135 +/- 9 GeV
• The Weak Gravity Conjecture and Scalar Fields
• Evidence for a Lattice Weak Gravity Conjecture
• Sharpening the Weak Gravity Conjecture with Dimensional Reduction
• The Weak Gravity Conjecture in three dimensions
• Neutrinoless double-beta decay. A brief review
• Natural Inflation and Quantum Gravity
• Casimir Energy and Radius Stabilization in Five and Six Dimensional Orbifolds
• Higgs inflation from Standard Model criticality
• Planckian Axions and the Weak Gravity Conjecture
• Weak Gravity Strongly Constrains Large-Field Axion Inflation
• Eliminating the optical depth nuisance from the CMB with 21 cm cosmology
• Bare Higgs mass at Planck scale
• Multidimensional extension of the generalized Chowla-Selberg formula
• On Axionic Field Ranges, Loopholes and the Weak Gravity Conjecture
• Relaxion Monodromy and the Weak Gravity Conjecture
• Quantum Horizons of the Standard Model Landscape
• Large-Field Inflation with Multiple Axions and the Weak Gravity Conjecture
• Warping the Weak Gravity Conjecture
• Dynamical compactification from de Sitter space
• A Chern-Simons Pandemic
• What is the Magnetic Weak Gravity Conjecture for Axions?
• Eternal Higgs inflation and cosmological constant problem
• Evidence of the Big Fix
• Constraints on the neutrino parameters by future cosmological 21cm line and precise CMB polarization observations
• PREdicted the Higgs Mass
• The fate of stringy AdS vacua and the WGC
• Below the Breitenlohner-Freedman bound in the nonrelativistic AdS/CFT correspondence
• Bubbles of Nothing and Supersymmetric Compactifications
• Standard Model Vacua for Two-dimensional Compactifications
• Weak Scale From the Maximum Entropy Principle
• Natural solution to the naturalness problem -- Universe does fine-tuning
• Standard model with compactified spatial dimensions
• Finite Temperature Structure of the Compactified Standard Model

Cited by in corpus (41)

• The Swampland: Introduction and Review
• Tensionless Strings and the Weak Gravity Conjecture
• A Stringy Test of the Scalar Weak Gravity Conjecture
• Weak Gravity Conjecture from Unitarity and Causality
• A Tower Weak Gravity Conjecture from Infrared Consistency
• Merging the Weak Gravity and Distance Conjectures Using BPS Extremal Black Holes
• Modular Fluxes, Elliptic Genera, and Weak Gravity Conjectures in Four Dimensions
• The String Landscape, the Swampland, and the Missing Corner
• Scalar Fields, Hierarchical UV/IR Mixing and The Weak Gravity Conjecture
• The FL bound and its phenomenological implications
• Modular Symmetries and the Swampland Conjectures
• A Strong Scalar Weak Gravity Conjecture and Some Implications
• Complexity is Simple
• Fine Tuning, Sequestering, and the Swampland
• Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism
• The Fundamental Need for a SM Higgs and the Weak Gravity Conjecture
• Swampland Constraints on Neutrino Masses
• AdS-phobia, the WGC, the Standard Model and Supersymmetry
• Minimal Surfaces and Weak Gravity
• Higgs Criticality beyond the Standard Model
• A dS obstruction and its phenomenological consequences
• Pole N-flation
• The Weak Scale from Weak Gravity
• IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
• Type IIB flux compactifications with $h^{1,1}=0$
• Modular Curves and the Refined Distance Conjecture
• Revisiting the Number-Theory Dark Matter Scenario and the Weak Gravity Conjecture
• Fermion masses and mixings in the supersymmetric Pati-Salam landscape from Intersecting D6-Branes
• Axion species scale and axion weak gravity conjecture-like bound
• Why The Cosmological Constant is a Boundary Condition
• Radiative stability of tiny cosmological constant from the Swampland and quantized compactification
• The Hierarchy Problem: From the Fundamentals to the Frontiers
• 4D dS vacua from AdS vacua of type IIB string theory and AdS distance conjecture
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• AdS Swampland Conjectures and Light Fermions
• Fermion Masses and Mixings in String Theory with Dirac Neutrinos
• Further swampland constraint on Dirac Neutrino
• Weighing the Vacuum Energy
• The Multiple Point Principle and Extended Higgs Sectors
• Compactifications of String/M-Theory and the Swampland: A Study of the AdS${}_{\text{4}}$ Mass Spectrum of Eleven-Dimensional Supergravity on the Squashed Seven-Sphere
• Species scale associated with Weinberg operator and bound on Majorana neutrino mass