Relating Berkovits and $A_\infty$ Superstring Field Theories; Small Hilbert Space Perspective

TL;DR

This paper explores the connection between Berkovits and $A_ abla$ superstring field theories from the small Hilbert space perspective, highlighting the algebraic structures linking them.

Contribution

It provides a new perspective on the relation between Berkovits and $A_ abla$ superstring field theories focusing on small Hilbert space and $A_ abla$ structures.

Findings

Establishes the relation between the two theories via small Hilbert space.

Highlights the role of $A_ abla$ structures in connecting the theories.

Provides a conceptual framework for understanding superstring field theory relations.

Abstract

In a previous paper it was shown that the recently constructed action for open superstring field theory based on $A_\infty$ algebras can be re-written in Wess-Zumino-Witten-like form, thus establishing its relation to Berkovits' open superstring field theory. In this paper we explain the relation between these two theories from a different perspective which emphasizes the small Hilbert space, and in particular the relation between the $A_\infty$ structures on both sides.