Nonlinear realizations of superconformal and W algebras as embeddings of strings

TL;DR

This paper introduces a straightforward method to construct representations of superconformal and W algebras using their subalgebras and Nambu-Goldstone fields, enabling new and known string and superstring embeddings with world-sheet symmetries.

Contribution

It presents a novel, simple approach for embedding strings and superstrings into superconformal and W algebras, including new embeddings like the bosonic string with U(1) symmetry into N=2 superstring.

Findings

Reproduces known string embeddings

Introduces new embeddings, e.g., bosonic string with U(1) into N=2 superstring

Provides a natural interpretation of the linearization of W_3^{(2)} algebra as string embedding

Abstract

We propose a simple method for constructing representations of (super)conformal and nonlinear 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 nonlinear $W_3^{(2)}$ 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.