Dilaton field induces commutative Dp-brane coordinate

TL;DR

This paper explores how a linear dilaton field affects the non-commutative geometry of Dp-branes, revealing that it can induce commutativity in certain directions by modifying the world-sheet metric.

Contribution

It introduces the impact of a linear dilaton field on Dp-brane non-commutativity, showing the conformal metric component as a new variable influencing coordinate commutativity.

Findings

Dilaton field can induce commutativity in directions orthogonal to the hyperplane.

The conformal part of the world-sheet metric acts as a new non-commutative variable.

In the presence of a linear dilaton, some coordinates become commutative.

Abstract

It is well known that space-time coordinates and corresponding Dp-brane world-volume become non-commutative, if open string ends on Dp-brane with Neveu-Schwarz background field $B_{\mu \nu}$. In this paper we extend these considerations including the dilaton field $\Phi$, linear in coordinates $x^\mu$. In that case the conformal part of the world-sheet metric appears as new non-commutative variable and the coordinate in direction orthogonal to the hyper plane $\Phi = const$, becomes commutative.