Open Superstring and Noncommutative Geometry

TL;DR

This paper quantizes open superstrings in a D-brane background with a B-field, revealing noncommutative geometry in superspace and deriving an effective Hamiltonian with a modified metric.

Contribution

It extends noncommutative geometry to superstrings by solving boundary constraints and deriving an effective Hamiltonian in superspace.

Findings

Noncommutative geometry extends to superspace in superstring theory.

The Hamiltonian is equivalent to a free superstring Hamiltonian with an effective metric G.

Constraints lead to a consistent quantization of superstrings in B-field backgrounds.

Abstract

We perform canonical quantization of the open Neveu-Schwarz-Ramond (NSR) superstrings in the background of a D-brane with the NS B-field. If we choose the mixed boundary condition as a primary constraint, it generates a set of secondary constraints. These constraints are easily solved and as a result, the noncommutative geometry in the bosonic string theory is extended to the superspace. Solving the constraint conditions we also find that the Hamiltonian for the superstring is equivalent to a free superstring Hamiltonian on the target space with the effective open string metric G.