Classical and quantum extended superconformal algebra

Abstract

The integrable supersymmetric Toda field theories enable us to construct several infinite series of the extended N = 1 and N = 2 superconformal algebras. In particular, in the cases of two series of the extended superconformal algebras associated with sl( n + 3| n) and osp(2 n ± 1| n), we find the supersymmetric Miura transformations. The classical extended superconformal algebras are realized as the Poisson bracket structure among the coefficients of a superdifferential operator. We also obtain the exotic minimal discrete series of the osp(3|2) quantum extended N = 1 superconformal algebra. This minimal series is different from those known so far in the sense that the corresponding central charge has no upper bound.