Fermionic anticommutators for open superstrings in the presence of antisymmetric tensor field

TL;DR

This paper develops the fermionic anticommutator algebra for open superstrings with antisymmetric tensor fields, employing Dirac and symplectic quantization methods to incorporate boundary conditions as constraints.

Contribution

It introduces a novel approach to handle boundary conditions as constraints using symplectic quantization with discretized actions.

Findings

Boundary conditions treated as zero modes of the symplectic matrix

Successful derivation of fermionic anticommutator algebra in this context

Application of both Dirac and symplectic quantization methods

Abstract

We build up the anticommutator algebra for the fermionic coordinates of open superstrings attached to branes with antisymmetric tensor fields. We use both Dirac quantization and the symplectic Faddeev Jackiw approach. In the symplectic case we find a way of generating the boundary conditions as zero modes of the symplectic matrix by taking a discretized form of the action and adding terms that vanish in the continuous limit. This way boundary conditions can be handled as constraints.