We reconstruct a complete type II superstring field theory with L-infinity structure in a symmetric way concerning the left- and right-moving sectors. Based on the new construction, we show again that the tree-level S-matrix agrees with that obtained
using the first-quantization method. Not only is this a simple and elegant reconstruction, but it also enables the action to be mapped to that in the WZW-like superstring field theory, which has not yet been constructed and fills the only gap in the WZW-like formulation.
We show that the tree-level S-matrices of the superstring field theories based on the homotopy-algebra structure agree with those obtained in the first-quantized formulation. The proof is given in detail for the heterotic string field theory. The ext
ensions to the type II and open superstring field theories are straightforward.
The gauge-fixing problem of modified cubic open superstring field theory is discussed in detail both for the Ramond and Neveu-Schwarz sectors in the Batalin-Vilkovisky (BV) framework. We prove for the first time that the same form of action as the cl
assical gauge-invariant one with the ghost-number constraint on the string field relaxed gives the master action satisfying the BV master equation. This is achieved by identifying independent component fields based on the analysis of the kernel structure of the inverse picture changing operator. The explicit gauge-fixing conditions for the component fields are discussed. In a kind of $b_0=0$ gauge, we explicitly obtain the NS propagator which has poles at the zeros of the Virasoro operator $L_0$.
