ace-time translation $\delta_p$, up to the equations of motion and gauge transformation, except for a nonlinear transformation $\delta_{\tilde{p}}$ that can be absorbed into the gauge transformation only at the linearized level. Thus the supersymmetry algebra holds only on the physical states, and hence the physical S-matrix, defined by the asymptotic string fields under appropriate assumptions on asymptotic properties of the string fields. Although this extra symmetry is unphysical in this sense, it is nontrivial in the total Hilbert space including unphysical degrees of freedom. It produces further unphysical symmetries by taking commutators with supersymmetries or themselves successively. We have a sequence of unphysical symmetries corresponding to the first-quantized charges obtained by taking successive commutators of the supercharge and the unconventional translation charge with picture number $p=-1$. Section 5 is devoted to summary and discussion, and two appendices are added. In Appendix A, we summarize the conventions for the $SO(1,9)$ spinor and the Ramond ground states, which are needed to identify the physical spectrum although they do not appear in this paper explicitly. The triviality of the extra transformation in the Ramond sector, which remains to be shown, is given in Appendix B. Further nonlinear transformations obtained by taking the commutator of two unphysical transformations, $[\delta_{\tilde{p}_1},\delta_{\tilde{p}_2}]$ are also discussed. All the extra symmetries obtained by taking commutators with $\delta_{\mathcal{S}}$ or $\delta_{\tilde{p}}$ repeatedly are shown to be unphysical.

Complete gauge-invariant action
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On the basis of the Ramond-Neveu-Schwarz (RNS) formulation of superstring theory, an open superstring field is a state in the conformal field theory (CFT) consisting of the matter sector, the reparametrization ghost sector, and the superconformal ghost sector. We assume in this paper that the background space-time is ten-dimensional Minkowski 