Supersymmetric extended string field theory in NSn sector and NSn − 1–R sector

We construct a class of quadratic gauge invariant actions for extended string fields defined on the tensor product of open superstring state space for multiple open string Neveu–Schwarz (NS) sectors with or without one Ramond (R) sector. The basic idea is the same as for the bosonic extended string field theory developed by the authors [1]. The theory for NSnNSn sector and NSn−1NSn−1–R sector contains general n  -th rank tensor fields and (n−1)(n−1)-th rank spinor–tensor fields in the massless spectrum respectively. In principle, consistent gauge invariant actions for any generic type of 10-dimensional massive or massless tensor or spinor–tensor fields can be extracted from the theory. We discuss some simple examples of bosonic and fermionic massless actions.