Non-linear structures in non-critical NSR string

We investigate the Ward identities of the W∞ symmetry in the super-Liouville theory coupled to the super-conformal matter of central charge cM=1-2(p-q)2/pq. The theory is classified into two chiralities. For the positive chirality, all gravitationally dressed scaling operators are generated from the q-1 gravitational primaries by acting one of the ring generators in the R-sector on them repeatedly. After fixing the normalizations of the dressed scaling operators, we find that the Ward identities are expressed in the form of the usual Wq algebra constraints as in the bosonic case: Wn(k+1)γ=0, (k=1,...,q-1; n is an element of Z≥1-k), where the equations for even and odd n come from the currents in the NS- and the R-sector respectively. The non-linear terms come from the anomalous contributions at the boundaries of moduli space. The negative chirality is defined by interchanging the roles of p and q. Then we get the Wp algebra constraints. (author)