339 citations · 6k across the 162 of their papers we have counts for
138 papers · 1 filter
CIPro Package: Complete Intersections in Products of Projective Spaces and Line Bundles
Lara B. Anderson, Andrei Constantin, James Gray +3
CIPro is a Mathematica package for constructing and analyzing complete intersections in products of projective spaces and line bundles over such varieties. It computes properties o…
New Calabi-Yau Manifolds from Genetic Algorithms
Per Berglund, Yang-Hui He, Elli Heyes +3
Calabi-Yau manifolds can be obtained as hypersurfaces in toric varieties built from reflexive polytopes. We generate reflexive polytopes in various dimensions using a genetic algor…
Numerical spectra of the Laplacian for line bundles on Calabi-Yau hypersurfaces
Anthony Ashmore, Yang-Hui He, Elli Heyes +1
We give the first numerical calculation of the spectrum of the Laplacian acting on bundle-valued forms on a Calabi-Yau three-fold. Specifically, we show how to compute the approxim…
Crystal Melting, BPS Quivers and Plethystics
Jiakang Bao, Yang-Hui He, Ali Zahabi
We study the refined and unrefined crystal/BPS partition functions of D6-D2-D0 brane bound states for all toric Calabi-Yau threefolds without compact 4-cycles and some non-toric ex…
Brain Webs for Brane Webs
Guillermo Arias-Tamargo, Yang-Hui He, Elli Heyes +2
We propose a new technique for classifying 5d Superconformal Field Theories arising from brane webs in Type IIB String Theory, using technology from Machine Learning to identify di…
Machine Learning Calabi-Yau Hypersurfaces
David S. Berman, Yang-Hui He, Edward Hirst
We revisit the classic database of weighted-P4s which admit Calabi-Yau 3-fold hypersurfaces equipped with a diverse set of tools from the machine-learning toolbox. Unsupervised tec…
The World in a Grain of Sand: Condensing the String Vacuum Degeneracy
Yang-Hui He, Shailesh Lal, M. Zaid Zaz
We propose a novel approach toward the vacuum degeneracy problem of the string landscape, by finding an efficient measure of similarity amongst compactification scenarios. Using a…
Reflexions on Mahler: Dessins, Modularity and Gauge Theories
Jiakang Bao, Yang-Hui He, Ali Zahabi
We provide a unified framework of Mahler measure, dessins d'enfants, and gauge theory. With certain physically motivated Newton polynomials from reflexive polygons, the Mahler meas…
Machine Learning Line Bundle Connections
Anthony Ashmore, Rehan Deen, Yang-Hui He +1
We study the use of machine learning for finding numerical hermitian Yang-Mills connections on line bundles over Calabi-Yau manifolds. Defining an appropriate loss function and foc…
Some Open Questions in Quiver Gauge Theory
Jiakang Bao, Amihay Hanany, Yang-Hui He +1
Quivers, gauge theories and singular geometries are of great interest in both mathematics and physics. In this note, we collect a few open questions which have arisen in various re…
Mahler Measure for a Quiver Symphony
Jiakang Bao, Yang-Hui He, Ali Zahabi
Adopting the Mahler measure from number theory, we introduce it to toric quiver gauge theories, and study some of its salient features and physical implications. We propose that th…
Integrality, Duality and Finiteness in Combinatoric Topological Strings
Robert de Mello Koch, Yang-Hui He, Garreth Kemp +1
A remarkable result at the intersection of number theory and group theory states that the order of a finite group (denoted ) is divisible by the dimension of any irr…
Direct Integration for Multi-leg Amplitudes: Tips, Tricks, and When They Fail
Jacob L. Bourjaily, Yang-Hui He, Andrew J. McLeod +5
Direct hyperlogarithmic integration offers a strong alternative to differential equation methods for Feynman integration, particularly for multi-particle diagrams. We review a vari…
Hilbert Series, Machine Learning, and Applications to Physics
Jiakang Bao, Yang-Hui He, Edward Hirst +3
We describe how simple machine learning methods successfully predict geometric properties from Hilbert series (HS). Regressors predict embedding weights in projective space to ${\s…
Dessins d'Enfants, Seiberg-Witten Curves and Conformal Blocks
Jiakang Bao, Omar Foda, Yang-Hui He +4
We show how to map Grothendieck's dessins d'enfants to algebraic curves as Seiberg-Witten curves, then use the mirror map and the AGT map to obtain the corresponding 4d $\mathcal{N…
Universes as Big Data
Yang-Hui He
We briefly overview how, historically, string theory led theoretical physics first to precise problems in algebraic and differential geometry, and thence to computational geometry…
Machine Learning Lie Structures & Applications to Physics
Heng-Yu Chen, Yang-Hui He, Shailesh Lal +1
Classical and exceptional Lie algebras and their representations are among the most important tools in the analysis of symmetry in physical systems. In this letter we show how the…
Machine Learning Calabi-Yau Four-folds
Yang-Hui He, Andre Lukas
Hodge numbers of Calabi-Yau manifolds depend non-trivially on the underlying manifold data and they present an interesting challenge for machine learning. In this letter we conside…
Chiral Rings, Futaki Invariants, Plethystics, and Groebner Bases
Jiakang Bao, Yang-Hui He, Yan Xiao
We study chiral rings of 4d supersymmetric gauge theories via the notion of K-stability. We show that when using Hilbert series to perform the computations of Futak…
Machine Learning Etudes in Conformal Field Theories
Heng-Yu Chen, Yang-Hui He, Shailesh Lal +1
We demonstrate that various aspects of Conformal Field Theory are amenable to machine learning. Relatively modest feed-forward neural networks are able to distinguish between scale…
Calabi-Yau Spaces in the String Landscape
Yang-Hui He
Calabi-Yau spaces, or Kahler spaces admitting zero Ricci curvature, have played a pivotal role in theoretical physics and pure mathematics for the last half-century. In physics, th…
Quiver Mutations, Seiberg Duality and Machine Learning
Jiakang Bao, Sebastián Franco, Yang-Hui He +3
We initiate the study of applications of machine learning to Seiberg duality, focusing on the case of quiver gauge theories, a problem also of interest in mathematics in the contex…
Quiver Gauge Theories: Beyond Reflexivity
Jiakang Bao, Grace Beaney Colverd, Yang-Hui He
Reflexive polygons have been extensively studied in a variety of contexts in mathematics and physics. We generalize this programme by looking at the 45 different lattice polygons w…
Machine-Learning Dessins d'Enfants: Explorations via Modular and Seiberg-Witten Curves
Yang-Hui He, Edward Hirst, Toby Peterken
We apply machine-learning to the study of dessins d'enfants. Specifically, we investigate a class of dessins which reside at the intersection of the investigations of modular subgr…