Statistics on the Heterotic Landscape: Gauge Groups and Cosmological Constants of Four-Dimensional Heterotic Strings

Abstract

Recent developments in string theory have reinforced the notion that the space of stable supersymmetric and non-supersymmetric string vacua fills out a ``landscape'' whose features are largely unknown. It is then hoped that progress in extracting phenomenological predictions from string theory -- such as correlations between gauge groups, matter representations, potential values of the cosmological constant, and so forth -- can be achieved through statistical studies of these vacua. To date, most of the efforts in these directions have focused on Type I vacua. In this note, we present the first results of a statistical study of the heterotic landscape, focusing on more than 10^5 explicit non-supersymmetric tachyon-free heterotic string vacua and their associated gauge groups and one-loop cosmological constants. Although this study has several important limitations, we find a number of intriguing features which may be relevant for the heterotic landscape as a whole. These features include different probabilities and correlations for different possible gauge groups as functions of the number of orbifold twists. We also find a vast degeneracy amongst non-supersymmetric string models, leading to a severe reduction in the number of realizable values of the cosmological constant as compared with naive expectations. Finally, we also find strong correlations between cosmological constants and gauge groups which suggest that heterotic string models with extremely small cosmological constants are overwhelmingly more likely to exhibit the Standard-Model gauge group at the string scale than any of its grand-unified extensions. In all cases, heterotic worldsheet symmetries such as modular invariance provide important constraints that do not appear in corresponding studies of Type I vacua.

arXiv comment58 pages, LaTeX, 17 figures, 3 tables; v2: one new figure and references added

References in corpus (88)

• de Sitter Vacua in String Theory
• Hierarchies from Fluxes in String Compactifications
• Quantization of Four-form Fluxes and Dynamical Neutralization of the Cosmological Constant
• Systematics of Moduli Stabilisation in Calabi-Yau Flux Compactifications
• Supersymmetric Unification Without Low Energy Supersymmetry And Signatures for Fine-Tuning at the LHC
• Flux compactifications in string theory: a comprehensive review
• The statistics of string/M theory vacua
• The Anthropic Landscape of String Theory
• Toward Realistic Intersecting D-Brane Models
• Distributions of flux vacua
• Supersymmetry Breaking and alpha'-Corrections to Flux Induced Potentials
• The String Landscape and the Swampland
• Large-Volume Flux Compactifications: Moduli Spectrum and D3/D7 Soft Supersymmetry Breaking
• Soft Supersymmetry Breaking in KKLT Flux Compactification
• Moduli Stabilization from Fluxes in a Simple IIB Orientifold
• Predictions from Quantum Cosmology
• Counting Flux Vacua
• PeV-Scale Supersymmetry
• String Theory and the Path to Unification: A Review of Recent Developments
• Observational Consequences of a Landscape
• Distributions of nonsupersymmetric flux vacua
• Supersymmetric Standard Model Spectra from RCFT orientifolds
• Soft Supersymmetry Breaking in Calabi-Yau Orientifolds with D-branes and Fluxes
• Moduli Stabilization in Chiral Type IIB Orientifold Models with Fluxes
• Flux-induced SUSY-breaking soft terms
• Flux-induced SUSY-breaking soft terms on D7-D3 brane systems
• Saltatory Relaxation of the Cosmological Constant
• Chiral 4d string vacua with D-branes and NSNS and RR fluxes
• Building MSSM Flux Vacua
• Stringy corrections to Kahler potentials, SUSY breaking, and the cosmological constant problem
• SUSY Phenomenology of KKLT Flux Compactifications
• Supersymmetry Breaking, M-Theory and Fluxes
• The Statistics of Supersymmetric D-brane Models
• One in a Billion: MSSM-like D-Brane Statistics
• Computational complexity of the landscape I
• Is There A String Theory Landscape
• Enumerating Flux Vacua with Enhanced Symmetries
• MSSM vacua from Flux Compactifications
• Solutions to the cosmological constant problems
• Chiral Supersymmetric Standard Model Spectra from Orientifolds of Gepner Models
• Basic results in Vacuum Statistics
• On the Explicit Construction and Statistics of Calabi-Yau Flux Vacua
• Low Energy Supersymmetry From the Landscape
• Anthropic considerations in multiple domain theories and the scale of electroweak symmetry breaking
• On the Taxonomy of Flux Vacua
• Modular Invariance, Finiteness, and Misaligned Supersymmetry: New Constraints on the Numbers of Physical String States
• Large Hierarchies from Attractor Vacua
• Statistical analysis of the supersymmetry breaking scale
• A Priori Probability Distribution of the Cosmological Constant
• A Framework for the Landscape
• Gauge Coupling Unification in Realistic Free-Fermionic String Models
• Statistics of M theory Vacua
• Anthropic prediction for Lambda and the Q catastrophe
• Probabilities in the Bousso-Polchinski multiverse
• Making Ends Meet: String Unification and Low-Energy Data
• Branches of the Landscape
• String Theory, Misaligned Supersymmetry, and the Supertrace Constraints
• Density Perturbations and the Cosmological Constant from Inflationary Landscapes
• String Unification, Higher-Level Gauge Symmetries, and Exotic Hypercharge Normalizations
• Realizing Higher-Level Gauge Symmetries in String Theory: New Embeddings for String GUTs
• Standard-like Models as Type IIB Flux Vacua
• On Anthropic Solutions of the Cosmological Constant Problem
• Nonrenormalization of Flux Superpotentials in String Theory
• A Barren Landscape?
• Landskepticism: or Why Effective Potentials Don't Count String Models
• A Review of Distributions on the String Landscape
• Can we predict $\Lambda$ for the Non-SUSY sector of the Landscape ?
• Solving the Hierarchy Problem without Supersymmetry or Extra Dimensions: An Alternative Approach
• R Symmetries in the Landscape
• Landscape Cartography: A Coarse Survey of Gauge Group Rank and Stabilization of the Proton
• Spontaneous Creation of Inflationary Universes and the Cosmic Landscape
• Anthropic Distribution for Cosmological Constant and Primordial Density Perturbations
• Model Building and Phenomenology of Flux-Induced Supersymmetry Breaking on D3-branes
• New Constraints on SO(10) Model-Building from String Theory
• Surveying Standard Model Flux Vacua on $T^6/Z_2\times Z_2$
• A Calculable Toy Model of the Landscape
• Discretuum versus Continuum Dark Energy
• Random Polynomials and the Friendly Landscape
• Flux Vacua Statistics for Two-Parameter Calabi-Yau's
• $Z_N$ Orientifolds with Flux
• Random values of the cosmological constant
• ERRATA for "One-Loop Threshold Effects in String Unification"
• The Intermediate Scale Branch of the Landscape
• Asymmetric Non-Abelian Orbifolds and Model Building
• Living in the Multiverse
• A Possible Mechanism for Generating a Small Positive Cosmological Constant
• Possible Stabilization Mechanism with Bulk and Branes SO(N) Yang-Mills for Closed Universes
• Constraints on the Cosmological Constant in a Static Geometry from Periodicity in a Compact Fifth-Dimension

Cited by in corpus (90)

• Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
• Flux Compactification
• A Mini-Landscape of Exact MSSM Spectra in Heterotic Orbifolds
• The Heterotic Road to the MSSM with R parity
• Heterotic GUT and Standard Model Vacua from simply connected Calabi-Yau Manifolds
• D-brane Deconstructions in IIB Orientifolds
• Heterotic mini-landscape (II): completing the search for MSSM vacua in a Z_6 orbifold
• Physics of String Flux Compactifications
• Towards a Non-Supersymmetric String Phenomenology
• A Comprehensive Scan for Heterotic SU(5) GUT models
• The landscape of intersecting brane models
• Life at the Interface of Particle Physics and String Theory
• Massless Spectra of Three Generation U(N) Heterotic String Vacua
• Non-supersymmetric heterotic model building
• Spinor-Vector Duality in fermionic Z2XZ2 heterotic orbifold models
• Low Energy Supersymmetry from the Heterotic Landscape
• Exophobic Quasi-Realistic Heterotic String Vacua
• Classification of Heterotic Pati-Salam Models
• Genetic Algorithms and the Search for Viable String Vacua
• Mapping an Island in the Landscape
• Supersymmetry versus Gauge Symmetry on the Heterotic Landscape
• Spinor-Vector Duality in Heterotic SUSY Vacua
• Searching the Landscape of Flux Vacua with Genetic Algorithms
• The lightest visible-sector supersymmetric particle is likely to be unstable
• Non-Tachyonic Semi-Realistic Non-Supersymmetric Heterotic String Vacua
• Deep learning in the heterotic orbifold landscape
• On exponential suppression of the cosmological constant in non-SUSY strings at two loops and beyond
• Spinor-Vector Duality in N=2 Heterotic String Vacua
• Classification of Standard-like Heterotic-String Vacua
• Geography of Fields in Extra Dimensions: String Theory Lessons for Particle Physics
• Classification of Flipped SU(5) Heterotic-String Vacua
• Counting String Theory Standard Models
• The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning
• String Derived Exophobic SU(6)xSU(2) GUTs
• Stability, enhanced gauge symmetry and suppressed cosmological constant in 9D heterotic interpolating models
• Exploring the SO(32) Heterotic String
• Fighting the Floating Correlations: Expectations and Complications in Extracting Statistical Correlations from the String Theory Landscape
• Classification of Non-Supersymmetric Pati-Salam Heterotic String Models
• Towards the Classification of Tachyon-Free Models From Tachyonic Ten-Dimensional Heterotic String Vacua
• String Defects, Supersymmetry and the Swampland
• On interpolations from SUSY to non-SUSY strings and their properties
• Statistics of intersecting D-brane models on T^6/Z_6
• Searching for the Standard Model in the String Landscape : SUSY GUTs
• Pati-Salam Unification from Non-commutative Geometry and the TeV-scale $W_R$ boson
• The Higgs Mass, Superconnections and the TeV-scale Left-Right Symmetric Model
• Asymmetric Gepner Models (Revisited)
• The Noether-Lefschetz Problem and Gauge-Group-Resolved Landscapes: F-Theory on K3 x K3 as a Test Case
• Revealing systematics in phenomenologically viable flux vacua with reinforcement learning
• Seeing through the String Landscape - a String Hunter's Companion in Particle Physics and Cosmology
• Building a Nest at Tree Level: Classical Metastability and Non-Trivial Vacuum Structure in Supersymmetric Field Theories
• Grand Unification in the Heterotic Brane World
• Heterotic Weight Lifting
• Gauge sector statistics of intersecting D-brane models
• Non-supersymmetric Orientifolds of Gepner Models
• Contrast data mining for the MSSM from strings
• Correlation Classes on the Landscape: To What Extent is String Theory Predictive?
• Top quark mass coupling and classification of weakly-coupled heterotic superstring vacua
• The Higgs Mass and the Emergence of New Physics
• Free Fermion Orientifolds
• The Flipped SU(5) String Vacua Classification: A Variation Of The SO(10) Breaking Basis Vector
• Statistical Predictions From Anarchic Field Theory Landscapes
• Doublet-Triplet Splitting in Fertile Left-Right Symmetric Heterotic String Vacua
• On the Search for Low $W_0$
• Free Fermionic Heterotic Model Building and Root Systems
• On the Running of Gauge Couplings in String Theory
• Is SUSY Natural?
• Note on a NAHE Variation
• Non-SUSY Heterotic String Vacua of Gepner Models with Vanishing Cosmological Constant
• MSSM via Pati-Salam from Intersecting Branes on $T^6/({\mathbb{Z}}_2\times {\mathbb{Z}}_2^{\prime })$
• Constraints on $N_c$ in Extensions of the Standard Model
• Niemeier Lattices in the Free Fermionic Heterotic-String Formulation
• Initial Systematic Investigations of the Landscape of Low Layer NAHE Extensions
• Systematic Investigations of the Free Fermionic Heterotic String Gauge Group Statistics: Layer 1 Results
• Diversity in the Tail of the Intersecting Brane Landscape
• A Non-Standard String Embedding of E8
• Statistics in the Landscape of Intersecting Brane Models
• Phenomenology from the Landscape of String Vacua
• Cosmological Constant Seesaw in String/M-Theory
• Joint Statistics of Cosmological Constant and SUSY Breaking in Flux Vacua with Nilpotent Goldstino
• Topological Data Analysis for the String Landscape
• Big Numbers in String Theory
• Investigation into Compactified Dimensions: Casimir Energies and Phenomenological Aspects
• Towards classification of SO(10) heterotic string vacua
• Redundancies in Explicitly Constructed Ten Dimensional Heterotic String Models
• Calabi-Yau compactifications of non-supersymmetric heterotic string theory
• Setting the Stage for a Non-Supersymmetric UV-Complete String Phenomenology
• Constraints on the Cosmological Constant in a Static Geometry from Periodicity in a Compact Fifth-Dimension
• Gauge Models in D Dimensions
• Universe Decay, Inflation and the Large Eigenvalue of the Cosmological Constant Seesaw
• Ranks of gauge groups and an NP-complete problem on the Landscape