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

Parviz Haggi-Mani·Ulf Lindstrom·Maxim Zabzine
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Abstract

We discuss the non-linear sigma model representing a NSR open string in a curved background with non-zero $B_{μν}$-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 $A_μ$-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.

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Parviz Haggi-Mani, Ulf Lindstrom, Maxim Zabzine. 2000-04-13. Boundary Conditions, Supersymmetry and A-field Coupling for an Open String in a B-field Background. https://doi.org/10.1016/s0370-2693(00)00600-6

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