Noncommutative Open strings, D-brane and Duality

TL;DR

This paper explores the duality and noncommutative structures of open strings ending on D-branes with background fields, revealing symmetry invariances and connections to the Seiberg-Witten map.

Contribution

It demonstrates how to derive dual theories with different boundary conditions from noncommutative open string setups, highlighting symmetry invariances and the role of B-fields.

Findings

Hamiltonian invariance under noncompact symmetry groups

Duality transformation relates noncommutative and Dirichlet boundary conditions

Connection established between duality and Seiberg-Witten map

Abstract

We consider open strings ending on D-branes in the presence of constant metric, G, antisymmetric tensor, B and gauge field, A. The Hamiltonian is manifestly invariant under a global noncompact group; strikingly similar to toroidally compactified closed string Hamiltonian. The evolution equations for the string coordinates, $\{X^i \}$ and their dual partners, $\{Y_i \}$, are combined to obtain equations of motion invariant under the noncompact symmetry transformations. We show that one can start from a noncommutative theory, with nonvanishing G and B and mixed boundary conditions and then go over to a dual theory whose coordinates obey Dirichlet boundary conditions. It is possible to generate B-field by implementing the noncompact symmetry transformation. The connection between this duality transformation and Seiberg-Witten map is discussed.