Boundary Conditions, Supersymmetry and A-field Coupling for an Open String in a B-field Background

TL;DR

This paper investigates how boundary conditions and additional boundary terms affect supersymmetry in an open string theory with a B-field background, proposing a specific A-field coupling that preserves supersymmetry.

Contribution

It introduces a boundary term that restores supersymmetry in the presence of a B-field and analyzes the effects of A-field coupling on boundary conditions and supersymmetry preservation.

Findings

Boundary term restores supersymmetry with B-field.

A-field coupling modifies boundary conditions.

A novel A-field coupling respects supersymmetry and shift symmetry.

Abstract

We discuss the non-linear sigma model representing a NSR open string in a curved background with non-zero $B_{\mu\nu}$-field. With this coupling the theory is not automatically supersymmetric, due to boundary contributions. When B=0 supersymmetry is ensured by the conditions that follow as the boundary contribution to the field equations. We show that inclusion of a particular boundary term restores this state of affairs also in the presence of a $B$-field. The boundary conditions derived from the field equations in this case agree with those that have been proposed for constant $B$-field. A coupling to a boundary $A_\mu$-field will modify both the boundary conditions and affect the supersymmetry. It is shown that there is an $A$-coupling with non-standard fermionic part that respects both the supersymmetry and the shift symmetry (in the $B$ and $A$ fields), modulo the (modified) boundary conditions.