An alternative way to explain how non-commutativity arises in the bosonic string theory

TL;DR

This paper explores an alternative explanation for the emergence of non-commutativity in bosonic string theory, linking it to non-commutative harmonic oscillators and D3-branes with magnetic fields.

Contribution

It introduces a novel approach by deriving non-commutative string theory from a non-commutative harmonic oscillator using Bopp's shifts matrix method.

Findings

Non-commutative harmonic oscillator obtained via Bopp's shifts.

Mapping of non-commutative oscillator to bosonic string theory on D3-brane.

Provides a new perspective on non-commutativity in string theory.

Abstract

In this work we will investigate how the non-commutativity arises into the string theory, \textit{i.e.}, how the bosonic string theory attaches to a D3-brane in the presence of magnetic fields. In order to accomplish the proposal, we departure from the commutative two-dimensional harmonic oscillator, which after the application of the general Bopp's shifts Matrix Method, the non-commutative version of the two-dimensional harmonic oscillator is obtained. After that, this non-commutative harmonic oscillator will be mapped into the bosonic string theory in the light cone frame, which it now appears as a bosonic string theory attached to a D3-brane.