The multi-pole Neveu-Schwarz algebra on Riemann supersphere

According to the Riemann-Roch theorem, we construct bases H-n(i) and N-m(j), for the meromorphic λ = -1 and λ = -1/2 differentials on the Riemann sphere S2. The dual bases, A-n(i) and D-m(j), of these meromorphic λ differentials on Cr curves are defined. Expanding the component fields TB(z) and TF(z) of the stress-energy tensor T(z) in the superconformal field theory by the dual bases A-n(i) and D-m(j), respectively, we obtain a series of expanding coefficients. The commutation relations among these coefficients are given explicitly, which is just the multi-pole Neveu-Schwarz algebra with central extensions on Riemann supersphere S-circumflex2. Physical implications of the algebra are also discussed. (author). 9 refs