(1+p)-dimensional open D (p−2) brane theories

Abstract

The dynamics of a Dp-brane can be described either by an open string ending on this brane or by an open D (p−2)-brane ending on the same Dp-brane. The ends of the open string couple to a Dp-brane worldvolume gauge field while the boundary of the open D (p−2)-brane couples to a (p−2)-form worldvolume potential whose field strength is Poincaré dual to that of the gauge field on the Dp-brane worldvolume. With this in mind, we find that the Poincaré dual of the fixed rank-2 magnetic field used in defining a (1+p)-dimensional noncommutative Yang-Mills (NCYM) gives precisely a near-critical electric field for the open D (p−2)-brane. We therefore find (1+p)-dimensional open D (p−2)-brane theories along the same line as for obtaining noncommutative open string theories (NCOS), OM theory and open Dp-brane theories (ODp) from NS5 brane. Similarly, the Poincaré dual of the near-critical electric field used in defining a (1+p)-dimensional NCOS gives a fixed magnetic-like field. This field along with the same bulk field scalings defines a (1+p)-dimensional noncommutative field theory. In the same spirit, we can have various (1 + 5)-dimensional noncommutative field theories resulting from the existence of ODp if the description of open D (4−p)-brane ending on the NS5 brane is insisted.