On-shell equivalence of two formulations for superstring field theory

Abstract

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

32 pages

References in corpus (2)

• NS-NS Sector of Closed Superstring Field Theory
• $A_{\infty }$ structure from the Berkovits formulation of open superstring field theory