is nontrivial in the total Hilbert space including unphysical degrees of freedom.

In any case, except for such an unphysical complexity, we have now understood how space-time supersymmetry is realized in superstring field theory, and therefore are ready to study various consequences of space-time supersymmetry[@Kishimoto:2005bs] on a firm basis. We have to (re)analyze them precisely using the techniques developed in conventional quantum field theory.[^7] We hope to report on them in the near future.

Acknowledgements {#acknowledgements .unnumbered}
================

The author would like to give special thanks to Ted Erler for helpful discussion, that was essential for clarifying the structure of the supersymmetry algebra in the large Hilbert space. The main part of the work was completed at the workshop on “String Field Theory and Related Aspects VIII” held at ICTP, SAIFR in São Paulo, Brazil. The author also thanks to the organizers, particularly Nathan Berkovits, for their hospitality and for providing a stimulating atmosphere.

Spinor conventions and Ramond ground states {#convention}
===========================================

In this paper, although it is mostly implicit, we adopt the chiral representation for $SO(1,9)$ gamma matrices $\Gamma^\mu$, in which $\Gamma^\mu$ is given by $$\Gamma^\mu\ =\ 
\begin{pmatrix}
 0 & (\gamma^\mu)_{\alpha\dot{\beta}}\\
(\bar{\gamma}^\mu)^{\dot{\alpha}\beta} & 0
\end{pmatrix}\,,$$ where $\gamma^\mu$ and $\bar{\gamma}^\mu$ satisfy $${(\gamma^\mu\bar{\gamma}^\nu + \gamma^\nu\bar{\gamma}^\mu)_\alpha}^\beta
=\ 2\eta^{\mu\nu}{\delta_\alpha}^\beta\,,\qquad
 {(\bar{\gamma}^\mu\gamma^\nu + \bar{\gamma}^\nu\gamma^\mu)^{\dot{\alpha}}}_{\dot{\beta}}
=\ 2\eta^{\mu\nu}{\delta^{\dot{\alpha}}}_{\dot{\beta}}\,.
$$ The charge conjugation matrix $\mathcal{C}$ satisfies the relations $$(\Gamma^\mu)^T\ =\ -\mathcal{C}\Gamma^\mu\mathcal{C}^{-1},\qquad
\mathcal{C}^T\ =\ -\mathcal{C}\,,$$ and is given in the chiral representation by $$\mathcal{C}\ =\
\begin{pmatrix}
 0 & {C^\alpha}_{\dot