Degenerate representations in supersymmetric theories (Q1070024)

The supersymmetric Neveu-Schwarz extension of the Virasoro algebra is studied. A representation based on a special combination, [\(\Phi\),\(\Psi\),0], of chiral superfields is considered, leading to an explicit superspace realisation of the fermionic generators, \(G_{\nu}\), in terms of supercovariant derivatives. The singular part of operator product expansions are used to define primary multiplets, \([\Phi,G_{- }\Phi]\), and related reducible Verma modules. The reducibility is associated with the phenomenon of degeneracy signified by the existence of null vectors \({\tilde \Psi}\) at various levels in the module. Differential relations between various correlation functions in these degenerate representations are derived.