Non-commutative Dp-Brane in General Background Fields

TL;DR

This paper explores how various background fields influence the non-commutative geometry of open strings attached to Dp-branes, including mode-dependent effects inspired by tachyon fields.

Contribution

It provides a detailed analysis of non-commutativity parameters, open string metrics, and mode-dependent effects in complex background field configurations.

Findings

Non-commutativity depends on background fields

Mode-dependent non-commutativity influenced by tachyon

Special cases reveal unique geometric properties

Abstract

We investigate non-commutativity of open strings, attached to a D$p$-brane, in the presence of the linear dilaton, tachyon, U(1) gauge field as well as constant anti-symmetric $B$-field backgrounds. Non-commutativity parameter, open string metric and some special cases will be studied. Mode-dependent non-commutativity, inspired by the tachyon field, will be discussed in detail.