Lectures on open strings, and noncommutative gauge fields

TL;DR

This paper explores the formulation of gauge theories on D-branes in flat and curved space-times, analyzing solutions to their equations of motion and Dirac equations, with extensions to complex geometries like orbifolds and K3 surfaces.

Contribution

It provides a background independent approach to gauge theories on D-branes and discusses solutions and generalizations to various curved geometries.

Findings

Solutions to equations of motion are presented.

Analysis of Dirac equation solutions in these backgrounds.

Extensions to orbifolds, conifolds, and K3 surfaces are discussed.

Abstract

The background independent formulation of the gauge theories on D-branes in flat space-time is considered, some examples of the solutions of their equations of motion are presented, the solutions of Dirac equation in these backgrounds are analyzed, and the generalizations to the curved spaces, like orbifolds, conifolds, and K3 surfaces, are discussed.