On noncommutative Nahm transform

TL;DR

This paper explores the noncommutative Nahm transform, extending the classical theory to noncommutative tori inspired by D-brane physics and noncommutative geometry.

Contribution

It introduces a noncommutative analogue of the Nahm transform specifically for instantons on the noncommutative torus, linking physics and advanced geometry.

Findings

Established a noncommutative version of the Nahm transform.

Connected noncommutative instantons with D-brane physics.

Provided mathematical framework for noncommutative gauge theories.

Abstract

Motivated by the recently observed relation between the physics of $D$-branes in the background of $B$-field and the noncommutative geometry we study the analogue of Nahm transform for the instantons on the noncommutative torus.