Comments on complete actions for open superstring field theory

We clarify a Wess-Zumino-Wtten-like structure including Ramond fields and propose one systematic way to construct gauge invariant actions: Wess-Zumino-Witten-like complete action $S_{\mathrm{W}\mathrm{Z}\mathrm{W}}$. We show that Kunitomo-Okawa’s action proposed in arXiv:1508.00366 can obtain a topological parameter dependence of Ramond fields and belongs to our WZW-like framework. In this framework, once a WZW-like functional $$\mathcal{A}${\eta } = $\mathcal{A}${\eta } [\Psi ]$ofadynamicalstringfield$\Psi $ is constructed, we obtain one realization of $S_{\mathrm{W}\mathrm{Z}\mathrm{W}}$ parametrized by $\mathrm{\Psi }$. On the basis of this way, we construct an action $\tilde{S}$ whose on-shell condition is equivalent to the Ramond equations of motion proposed in arXiv:1506.05774. Using these results, we provide the equivalence of two these theories: arXiv:1508.00366 and arXiv:1506.05774.