THE CONFORMAL BOOTSTRAP AND SUPER W-ALGEBRAS

We undertake a systematic study of the possible extensions of the N = 1 super Virasoro algebra by a superprimary field of spin 1/2 less-than-or-equal-to DELTA less-than-or-equal-to 7/2. Besides new extensions, which exist only for specific values of the central charge, we find a new nonlinear algebra (super W2) generated by a spin 2 superprimary which is associative for all values of the central charge. Furthermore, the spin 3 extension is argued to be the symmetry algebra of the m = 6 super Virasoro unitary minimal model, by exhibiting the (A7, D4)-type modular invariant as diagonal in terms of extended characters.