A consistent light-cone-gauge superstring field theory

Extending a recent development in the bosonic string field theory, we construct a map from the Witten-type gauge-invariant superstring field theory based on an $A_{\infty}$ structure to a light-cone-gauge superstring field theory via two intermediate theories, which we call the Kaku-type and Kugo-Zwiebach-type superstring field theories. We find that a naive extension only gives us an inconsistent light-cone-gauge theory that suffers from the well-known problem caused by divergence due to collisions of local operators. However, we also find that this difficulty may be resolved by considering the stubbed theory and propose it as a consistent light-cone-gauge superstring field theory. The result possibly gives a proof of the unitarity of the Witten-type superstring field theory.