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arXiv · 1506.06657

On-shell equivalence of two formulations for superstring field theory

Keiyu Goto·Hiroaki Matsunaga
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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.

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Keiyu Goto, Hiroaki Matsunaga. 2015-06-18. On-shell equivalence of two formulations for superstring field theory. https://arxiv.org/abs/1506.06657

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