Machine Learning Regularization for the Minimum Volume Formula of Toric Calabi-Yau 3-folds

Abstract

We present a collection of explicit formulas for the minimum volume of Sasaki-Einstein 5-manifolds. The cone over these 5-manifolds is a toric Calabi-Yau 3-fold. These toric Calabi-Yau 3-folds are associated with an infinite class of 4d N=1 supersymmetric gauge theories, which are realized as worldvolume theories of D3-branes probing the toric Calabi-Yau 3-folds. Under the AdS/CFT correspondence, the minimum volume of the Sasaki-Einstein base is inversely proportional to the central charge of the corresponding 4d N=1 superconformal field theories. The presented formulas for the minimum volume are in terms of geometric invariants of the toric Calabi-Yau 3-folds. These explicit results are derived by implementing machine learning regularization techniques that advance beyond previous applications of machine learning for determining the minimum volume. Moreover, the use of machine learning regularization allows us to present interpretable and explainable formulas for the minimum volume. Our work confirms that, even for extensive sets of toric Calabi-Yau 3-folds, the proposed formulas approximate the minimum volume with remarkable accuracy.

arXiv comment15 pages, 9 figures, 4 tables

References in corpus (43)

• Deep Learning in Neural Networks: An Overview
• The Holographic Weyl anomaly
• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• Phases of $N=2$ Theories In Two Dimensions
• Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity
• The Exact Superconformal R-Symmetry Maximizes a
• On Conformal Theories in Four Dimensions
• Gauge Theories from Toric Geometry and Brane Tilings
• Orbifold Resolution by D-Branes
• D-Brane Gauge Theories from Toric Singularities and Toric Duality
• An Infinite Family of Superconformal Quiver Gauge Theories with Sasaki-Einstein Duals
• Brane Dimers and Quiver Gauge Theories
• Counting Gauge Invariants: the Plethystic Program
• Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics
• Sasaki-Einstein Manifolds and Volume Minimisation
• Einstein manifolds and conformal field theories
• The Geometric Dual of a-maximisation for Toric Sasaki-Einstein Manifolds
• Toric Geometry, Sasaki-Einstein Manifolds and a New Infinite Class of AdS/CFT Duals
• Toric Duality Is Seiberg Duality
• Phase Structure of D-brane Gauge Theories and Toric Duality
• From Sasaki-Einstein spaces to quivers via BPS geodesics: Lpqr
• The Master Space of N=1 Gauge Theories
• The dual superconformal theory for Lpqr manifolds
• R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization
• Machine Learning of Calabi-Yau Volumes
• Machine Learning in the String Landscape
• Counting Chiral Operators in Quiver Gauge Theories
• Evolving neural networks with genetic algorithms to study the String Landscape
• Machine Learning CICY Threefolds
• Neural Networks and Quantum Field Theory
• From Toric Geometry to Quiver Gauge Theory: the Equivalence of a-maximization and Z-minimization
• Searching the Landscape of Flux Vacua with Genetic Algorithms
• Mastering the Master Space
• Deep Learning the Hyperbolic Volume of a Knot
• Machine Learning Line Bundle Cohomology
• Molien Function for Duality
• Machine Learning Calabi-Yau Hypersurfaces
• Machine Learning Calabi-Yau Four-folds
• Machine learning for complete intersection Calabi-Yau manifolds: a methodological study
• Evolving Heterotic Gauge Backgrounds: Genetic Algorithms versus Reinforcement Learning
• Calabi-Yau Volumes and Reflexive Polytopes
• Neurons on Amoebae
• Unsupervised Machine Learning Techniques for Exploring Tropical Coamoeba, Brane Tilings and Seiberg Duality

Cited by in corpus (7)

• Learning BPS Spectra and the Gap Conjecture
• Hamiltonian Neural Networks approach to fuzzball geodesics
• Generative AI for Brane Configurations and Coamoeba
• Calabi-Yau Four/Five/Six-folds as ${\mathbb{P}}_{\text{w}}^n$ Hypersurfaces: Machine Learning, Approximation, and Generation
• Classification and Birational Equivalence of Dimer Integrable Systems for Reflexive Polygons
• Row and column detection complexities of character tables
• Learning 3-Manifold Triangulations