Comments on complete actions for open superstring field theory

TL;DR

This paper clarifies a Wess-Zumino-Witten-like structure for open superstring field theory, proposing a systematic construction of gauge-invariant actions that unify previous formulations and demonstrate their equivalence.

Contribution

It introduces a WZW-like framework for superstring field theory actions, unifying and clarifying previous approaches, and proves the equivalence of two existing theories.

Findings

Established a WZW-like structure including Ramond fields.

Constructed a gauge-invariant action $S_{WZW}$ within this framework.

Proved the equivalence of two previously proposed superstring field theories.

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.