Non-linear realizations of superconformal and W-algebras as embeddings of strings Original Research Article

We propose a simple method for constructing representations of (super) conformal and non-linear W-type algebras in terms of their subalgebras and corresponding Nambu-Goldstone fields. We apply it to N = 2 and N = 1 superconformal algebras and describe in this way various embeddings of strings and superstrings for which these algebras and their subalgebras define world-sheet symmetries. Besides reproducing the known examples, we present some new ones, in particular an embedding of the bosonic string with additional U(1) affine symmetry into N = 2 superstring. We also apply our method to the non-linear W3(2) algebra and demonstrate that the linearization procedure worked out for it some time ago gets a natural interpretation as a kind of string embedding. All these embeddings include the critical ones as particular cases.