Calabi-Yau manifolds from noncommutative Hermitian U(1) instantons

TL;DR

This paper demonstrates that Calabi-Yau manifolds can be derived as the commutative limit of six-dimensional noncommutative Hermitian U(1) instantons, suggesting a quantized perspective on these complex geometries.

Contribution

It introduces a novel connection between noncommutative Hermitian U(1) instantons and Calabi-Yau manifolds, proposing that these instantons correspond to their quantized versions.

Findings

Calabi-Yau manifolds emerge from noncommutative instantons in the commutative limit.

Noncommutative Hermitian U(1) instantons are equivalent to quantized Calabi-Yau manifolds.

The work bridges noncommutative gauge theory and complex geometry.

Abstract

We show that Calabi-Yau manifolds are emergent from the commutative limit of six-dimensional noncommutative Hermitian U(1) instantons. Therefore we argue that the noncommutative Hermitian U(1) instantons correspond to quantized Calabi-Yau manifolds.