$A_\infty$ structure from the Berkovits formulation of open superstring field theory

TL;DR

This paper demonstrates how an $A_ Infty$-structured action for open superstring field theory, initially formulated in the small Hilbert space, can be transformed into a Wess-Zumino-Witten-like form and related to Berkovits' large Hilbert space formulation through gauge fixing and redefinition.

Contribution

It establishes a connection between the $A_ Infty$-structured small Hilbert space formulation and Berkovits' large Hilbert space formulation via gauge fixing and field redefinition.

Findings

Successfully reformulated the action into Wess-Zumino-Witten-like form

Established the relation between small and large Hilbert space formulations

Provided a new perspective on superstring field theory structures

Abstract

By formulating open superstring field theory based on the small Hilbert space of the superconformal ghost sector, an action for the Neveu-Schwarz sector with an $A_\infty$ structure has recently been constructed. We transform this action to the Wess-Zumino-Witten-like form and show that this theory is related to the Berkovits formulation of open superstring field theory based on the large Hilbert space by partial gauge fixing and field redefinition.