Dilaton field induces commutative Dp-brane coordinate

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 $B_{μν}$. In this paper we extend these considerations including the dilaton field $Φ$, linear in coordinates $x^μ$. 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 $Φ= const$, becomes commutative.