W-strings from N=2 Hamiltonian reduction and classification of N=2 super W-algebras

TL;DR

This paper develops an algebraic framework for string theory using Hamiltonian reduction of N=2 WZW models, classifies all embeddings of sl(1|2) into Lie superalgebras, and characterizes the resulting extended N=2 superconformal algebras and string theories.

Contribution

It provides a complete classification of all extended N=2 superconformal algebras derived from sl(1|2) embeddings in Lie superalgebras and explores their string theory implications.

Findings

Classified all embeddings of sl(1|2) into Lie superalgebras.

Extended N=2 superconformal algebras characterized and classified.

Derived the BRST structure for a class of string theories.

Abstract

We present an algebraic approach to string theory, using a Hamiltonian reduction of N=2 WZW models. An embedding of sl(1|2) in a Lie superalgebra determines a niltopent subalgebra. Chirally gauging this subalgebra in the corresponding WZW action leads to an extension of the N=2 superconformal algebra. We classify all the embeddings of sl(1|2) into Lie superalgebras: this provides an exhaustive classification and characterization of all extended N=2 superconformal algebras. Then, twisting these algebras, we obtain the BRST structure of a string theory. We characterize and classify all the string theories which can be obtained in this way. Based on a common work of E. Ragoucy, A. Sevrin and P. Sorba, presented by E. Ragoucy at ``Extended and Quantum Algebras and their Applications to Physics'', Nankai Institute in Tianjin (China) August 19-24 1996