Strings from $N=2$ Gauged Wess-Zumino-Witten Models

Abstract

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.

50 pages, LaTeX

References in corpus (6)

• On the Uniqueness of String Theory
• Extensions of the Virasoro Algebra and Gauged WZW Models
• Quantum Hamiltonian Reduction in Superspace Formalism
• The Kazhdan-Lusztig conjecture for W-algebras
• Superstrings from Hamiltonian Reduction
• Topological Strings from WZW Models

Cited by in corpus (8)

• Dictionary on Lie Superalgebras
• Higher spin AdS_3 supergravity and its dual CFT
• Dualities from higher-spin supergravity
• Embedding Diagrams of N=2 Verma Modules and Relaxed ^sl(2) Verma Modules
• The Non-Critical N=2 String is an sl(2|1) Theory
• Exact monopole instantons and cosmological solutions in string theory from abelian dimensional reduction
• An n=(1|1) super--Toda Model Based on OSp(1|4)
• Gauging Wess-Zumino-Witten Models