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In a previous paper it was shown that the recently constructed action foropen superstring field theory based on $A_\infty$ algebras can be re-written inWess-Zumino-Witten-like form, thus establishing its relation to Berkovits' opensuperstring field theory. In this paper we explain the relation between thesetwo theories from a different perspective which emphasizes the small Hilbertspace, and in particular the relation between the $A_\infty$ structures on bothsides.

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