Calabi-Yau manifold

A Calabi-Yau manifold is a compact Kähler manifold with vanishing first Chern class and a Ricci-flat metric. They are named after Eugenio Calabi, who proposed the conjecture that such metrics exist, and Shing-Tung Yau, who proved it in 1978. Calabi-Yau manifolds are the preferred compactification spaces in string theory, where their intricate topology determines the low-energy physics of the resulting four-dimensional theory — including the spectrum of particles and the structure of gauge interactions. Their Hodge numbers classify the possible topologies, and the study of their moduli spaces connects algebraic geometry to quantum gravity in ways that remain only partially understood.