(1 + p)-Dimensional Open D(p - 2) Brane Theories

TL;DR

This paper explores the relationship between open D-brane theories and noncommutative field theories, revealing how dualities and field configurations lead to new higher-dimensional noncommutative theories similar to NCOS and ODp frameworks.

Contribution

It introduces a novel connection between Poincare duals of magnetic and electric fields and the emergence of higher-dimensional open D-brane theories and noncommutative field theories.

Findings

Poincare duals of magnetic fields yield near-critical electric fields for open D-branes.

Near-critical electric fields correspond to fixed magnetic-like fields in noncommutative theories.

Various (1 + 5)-dimensional noncommutative field theories can arise from ODp configurations.

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 Poincare dual to that of the gauge field on the Dp-brane worldvolume. With this in mind, we find that the Poincare 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 Poincare 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.