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.

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

References in corpus (8)

• The Anthropic Landscape of String Theory
• The String Landscape and the Swampland
• Computational complexity of the landscape I
• Statistical analysis of the supersymmetry breaking scale
• Landskepticism: or Why Effective Potentials Don't Count String Models
• Anthropic Distribution for Cosmological Constant and Primordial Density Perturbations
• Random Polynomials and the Friendly Landscape
• A Possible Mechanism for Generating a Small Positive Cosmological Constant

Cited by in corpus (46)

• 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
• Physics of String Flux Compactifications
• Towards a Non-Supersymmetric String Phenomenology
• Non-supersymmetric heterotic model building
• Spinor-Vector Duality in fermionic Z2XZ2 heterotic orbifold models
• Low Energy Supersymmetry from the Heterotic Landscape
• Classification of Heterotic Pati-Salam Models
• Genetic Algorithms and the Search for Viable String Vacua
• Supersymmetry versus Gauge Symmetry on the Heterotic Landscape
• Spinor-Vector Duality in Heterotic SUSY Vacua
• Spinor-Vector Duality in N=2 Heterotic String Vacua
• Geography of Fields in Extra Dimensions: String Theory Lessons for Particle Physics
• Classification of Flipped SU(5) Heterotic-String Vacua
• Stability, enhanced gauge symmetry and suppressed cosmological constant in 9D heterotic interpolating models
• 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
• Statistics of intersecting D-brane models on T^6/Z_6
• The Higgs Mass, Superconnections and the TeV-scale Left-Right Symmetric Model
• 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
• Contrast data mining for the MSSM from strings
• Gauge sector statistics of intersecting D-brane models
• Non-supersymmetric Orientifolds of Gepner Models
• Top quark mass coupling and classification of weakly-coupled heterotic superstring vacua
• Free Fermion Orientifolds
• On the Search for Low $W_0$
• Is SUSY Natural?
• On the Running of Gauge Couplings in String Theory
• 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
• Phenomenology from the Landscape of String Vacua
• Statistics in the Landscape of Intersecting Brane Models
• Cosmological Constant Seesaw in String/M-Theory
• Topological Data Analysis for the String Landscape
• Joint Statistics of Cosmological Constant and SUSY Breaking in Flux Vacua with Nilpotent Goldstino
• Investigation into Compactified Dimensions: Casimir Energies and Phenomenological Aspects
• Universe Decay, Inflation and the Large Eigenvalue of the Cosmological Constant Seesaw
• Ranks of gauge groups and an NP-complete problem on the Landscape