On-shell equivalence of two formulations for superstring field theory

摘要: In this paper we derive the condition providing on-shell equivalence of $L_{\infty}$-type and WZW-like formulations for superstring field theory. We construct NS string products $L= \{L_{n}\}_{n=1}^{\infty}$ formulation shifted BRST operator $Q_{\mathcal{G}}$ in by similarity transformations $Q$. Utilizing transformations, can consider a morphism connecting $L_{\infty}$-algebras on both sides. It naturally induces redefinitions guarantees conditions two formulations. addition, have confirmed up to quartic order that also provides off-shell equivalence. Then partial-gauge-fixing giving $L_{\infty}$-relations appear.