Comments on the N = 2,3,4 superconformal algebras in two dimensions

Abstract We discuss the extended superconformal algebras (SCA's) in two dimensions. A general classification of the different algebras is presented. It is shown that the Neveu-Schwarz and the Ramond N = 2 SCA's are equivalent. We find two N = 3 SCA's and discuss their representations. Unitary highest weight representations of these algebras in terms of one boson and one fermion ( c = 3 2 are exhibited. We also find an infinite set of N = 4 SCA's and we comment on their representations.

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