Supersymmetry in Open Superstring Field Theory

TL;DR

This paper demonstrates how unbroken supersymmetries of a BPS D-brane are realized as invariances in open superstring field theory, linking algebraic structures to physical symmetries and scattering amplitudes.

Contribution

It provides a detailed analysis of supersymmetry invariance within the small Hilbert space framework of open superstring field theory, connecting algebraic and physical aspects.

Findings

Supersymmetry invariances are realized as symmetries of the cyclic A_infinity structure.

The supersymmetry algebra includes translations, gauge transformations, and on-shell vanishing symmetries.

Supersymmetry of the action implies supersymmetry of tree-level scattering amplitudes.

Abstract

We realize the 16 unbroken supersymmetries on a BPS D-brane as invariances of the action of the corresponding open superstring field theory. We work in the small Hilbert space approach, where a symmetry of the action translates into a symmetry of the associated cyclic $A_\infty$ structure. We compute the supersymmetry algebra, being careful to disentangle the components which produce a translation, a gauge transformation, and a symmetry transformation which vanishes on-shell. Via the minimal model theorem, we illustrate how supersymmetry of the action implies supersymmetry of the tree level open string scattering amplitudes.