Calabi-Yau metrics and string compactification

Abstract

Yau proved an existence theorem for Ricci-flat Kähler metrics in the 1970's, but we still have no closed form expressions for them. Nevertheless there are several ways to get approximate expressions, both numerical and analytical. We survey some of this work and explain how it can be used to obtain physical predictions from superstring theory.

10 pages. Version to appear in Nuclear Physics B special issue: 60 Years of Calabi Conjecture

References in corpus (5)

• Numerical Calabi-Yau metrics
• Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic
• Numerical Kaehler-Einstein metric on the third del Pezzo
• Numerical approximations to extremal metrics on toric surfaces
• Numerical Algorithms for Finding Balanced Metrics on Vector Bundles

Cited by in corpus (11)

• Machine learning Calabi-Yau metrics
• Numerical Calabi-Yau metrics from holomorphic networks
• Lectures on the Calabi-Yau Landscape
• Calabi-Yau Manifolds and SU(3) Structure
• General Markovian Equation for Scalar Fields in a Slowly Evolving Background
• Brane-Worlds and the Calabi-Yau Complex Structure Moduli
• String Corrected Spacetimes and SU(N)-Structure Manifolds
• Mink${}_4\times S^2$ Solutions of 10 and 11 Dimensional Supergravity
• The Implications of N = 2 Supergravity Cosmology On the Topology of the Calabi-Yau Manifold
• cymyc -- Calabi-Yau Metrics, Yukawas, and Curvature
• From Algebraic Geometry to Machine Learning