1995/11/07 by E. Ragoucy, A. Sevrin, Alexander Sevrin +1
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #hep-th
paper · pdf · doi:10.1007/bf02101674
published as Commun.Math.Phys. 181 (1996) 91 · 50 pages, LaTeX
arxiv created 1995/11/07 · openalex publication_date 1996/11/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present an algebraic approach to string theory. An embedding of sl(2|1) in a super Lie algebra together with a grading on the Lie algebra determines a nilpotent subalgebra of the super Lie algebra. Chirally gauging this subalgebra in the corresponding Wess-Zumino-Witten model, breaks the affine symmetry of the Wess-Zumino-Witten model to some extension of the N=2 superconformal algebra. The extension is completely determined by the sl(2|1) embedding. The realization of the superconformal algebra is determined by the grading. For a particular choice of grading, one obtains in this way, after twisting, the BRST structure of a string theory. We classify all embeddings of sl(2|1) into Lie super algebras and give a detailed account of the branching of the adjoint representation. This provides an exhaustive classification and characterization of both all extended N=2 superconformal algebras and all string theories which can be obtained in this way.