Noncommutative Deformation of Instantons

TL;DR

This paper constructs and analyzes instanton solutions on noncommutative Euclidean 4-space, demonstrating that their topological charge remains unchanged under deformation and exploring similar solutions on a noncommutative torus.

Contribution

It introduces a method to deform instanton solutions to noncommutative spaces and shows the preservation of instanton numbers under such deformations.

Findings

Noncommutative instantons have the same instanton number as commutative ones.

The instanton number is conjectured to be preserved under general noncommutative deformations.

Studied noncommutative instantons on T^4 with twisted boundary conditions.

Abstract

We construct instanton solutions on noncommutative Euclidean 4-space which are deformations of instanton solutions on commutative Euclidean 4-space. We show that the instanton numbers of these noncommutative instanton solutions coincide with the commutative solutions and conjecture that the instanton number in R^4 is preserved for general noncommutative deformations. We also study noncommutative deformation of instanton solutions on a T^4 with twisted boundary conditions.