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Toric geometry and local Calabi-Yau varieties: An introduction to toric geometry (for physicists)
TLDR
In this paper, the authors introduce toric geometry and describe toric local Calabi-Yau singularities as holomorphic quotients, and explain the gauged linear sigma-model (GLSM) Kahler quotient construction.Abstract:
These lecture notes are an introduction to toric geometry. Particular focus is put on the description of toric local Calabi-Yau varieties, such as needed in applications to the AdS/CFT correspondence in string theory. The point of view taken in these lectures is mostly algebro-geometric but no prior knowledge of algebraic geometry is assumed. After introducing the necessary mathematical definitions, we discuss the construction of toric varieties as holomorphic quotients. We discuss the resolution and deformation of toric Calabi-Yau singularities. We also explain the gauged linear sigma-model (GLSM) Kahler quotient construction.read more
Citations
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Journal ArticleDOI
Chiral flavors and M2-branes at toric CY4 singularities
TL;DR: In this paper, the authors extend the stringy derivation of N = 2 AdS4/CFT3 dualities to cases where the M-theory circle degenerates at complex codimension-two submanifolds of a toric conical CY4.
Journal ArticleDOI
Chiral flavors and M2-branes at toric CY4 singularities
TL;DR: In this article, the authors extend the stringy derivation of AdS4/CFT3 dualities to cases where the M-theory circle degenerates at complex codimension-two submanifolds of a toric conical CY4.
Journal ArticleDOI
Global F-theory models: instantons and gauge dynamics
Mirjam Cvetič,Mirjam Cvetič,Iñaki García-Etxebarria,Iñaki García-Etxebarria,James Halverson,James Halverson +5 more
TL;DR: In this paper, a compact F-theory GUT model is presented, in which D-brane instantons generate the top Yukawa coupling non-perturbatively.
Book
The Calabi–Yau Landscape: From Geometry, to Physics, to Machine Learning
TL;DR: In this paper, the authors present a pedagogical introduction to the recent advances in computational geometry, physical implications, and data science of Calabi-Yau manifolds aimed at the beginning research student.
Book ChapterDOI
Feynman integrals, toric geometry and mirror symmetry
TL;DR: In this paper, the maximal cut of a Feynman integral is a GKZ hypergeometric series and the minimal differential operator acting on it is a trilogarithm.
References
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Book
Principles of Algebraic Geometry
Phillip Griffiths,Joe Harris +1 more
TL;DR: In this paper, a comprehensive, self-contained treatment of complex manifold theory is presented, focusing on results applicable to projective varieties, and including discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex.
Book
Introduction to Toric Varieties.
TL;DR: In this article, a mini-course is presented to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications, concluding with Stanley's theorem characterizing the number of simplicies in each dimension in a convex simplicial polytope.
Journal ArticleDOI
Supergravity and a confining gauge theory: duality cascades and χSB-resolution of naked singularities
TL;DR: In this article, a non-singular pure-supergravity background dual to the field theory on all scales, with small curvature everywhere if the ‘t Hooft coupling gsM is large, was proposed.
Journal ArticleDOI
Phases of N = 2 theories in two dimensions
TL;DR: In this paper, a natural relation between sigma models based on Calabi-Yau hypersurfaces in weighted projective spaces and Landau-Ginzburg models is found.
Book
Mirror Symmetry
Eric Zaslow,Ravi Vakil,Kentaro Hori,Richard P. Thomas,Cumrun Vafa,Albrecht Klemm,Rahul Pandharipande,Sheldon Katz +7 more
TL;DR: In this paper, the authors proved mirror symmetry for supersymmetric sigma models on Calabi-Yau manifolds in 1+1 dimensions and showed that the equivalence of the gauged linear sigma model embedded in a theory with an enlarged gauge symmetry, with a Landau-Ginzburg theory of Toda type Standard R -> 1/R duality and dynamical generation of superpotential by vortices.