Abstract
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 $S_{\rm WZW}$. 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 $\mathcal{A}_{\eta } = \mathcal{A}_{\eta } [\Psi ]$ of a dynamical string field $\Psi $ is constructed, we obtain one realization of $S_{\rm WZW}$ parametrized by $\Psi $. On the basis of this way, we construct an action $\widetilde{S}$ 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.
Highlights
We show that one can add the t-dependence of Ramond string fields into the complete action proposed in [1] and make the t-dependence of the action “topological”, which leads us a natural idea of Wess-Zumino-Witten-like structure including Ramond fields
We show that our WZW-like complete action has so-called topological parameter dependence in section 2.1 and is gauge invariant in 2.2
We show that a complete action of open superstring field theory proposed in [1] can be written as
Summary
We use the same notation as [1]. First, we show that one can add a parameter dependence of R string fields into Kunitomo-Okawa’s action, and that the resultant action has topological parameter dependence. We use this restricted small Hilbert space HR as the state space of the Ramond string field. In this Kunitomo-Okawa’s action, only the NS field ΦNS(t) has a parameter dependence and the R field ΦR does not have it: ∂tΦNS(t) = 0 and ∂tΨR = 0, where a t-parametrized NS field ΦNS(t) is a path satisfying ΦNS(t = 0) = 0 and ΦNS(t = 1) = ΦNS on the state space. In the work of [1], all computations of the variation of the action, equations of motion, and gauge invariance heavily depend on the explicit form or properties of the linear map F on ΨR. As we will show these all computations are derived from WZW-like properties of the Ramond sector: (1.11), (1.12), and (1.14)
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