BFT embedding of noncommutative D-brane system

TL;DR

This paper applies the BFT scheme to convert second class constraints in noncommutative D-brane systems into first class constraints, revealing a way to recover commutative geometry and uncover new local symmetries.

Contribution

It introduces a novel BFT-based approach to analyze noncommutative geometry in D-brane systems, enabling the transition to commutative geometry via a new coordinate.

Findings

Introduction of a new coordinate y on D-brane

Recovery of commutative geometry from noncommutative setup

Identification of a new local symmetry in the action

Abstract

We study noncommutative geometry in the framework of the Batalin-Fradkin-Tyutin(BFT) scheme, which converts second class constraint system into first class one. In an open string theory noncommutative geometry appears due to the mixed boundary conditions having second class constraints, which arise in string theory with $D$-branes under a constant Neveu-Schwarz $B$-field. Introduction of a new coordinate $y$ on $D$-brane through BFT analysis allows us to obtain the commutative geometry with the help of the first class constraints, and the resulting action corresponding to the first class Hamiltonian in the BFT Hamiltonian formalism has a new local symmetry.