On SW-minimal models and N=1 supersymmetric Quantum Toda-field theories

Abstract

We construct free field representations of the $SW$-algebras SW(3/2,2) and SW(3/2,3/2,2) by using the corresponding Toda-Field-Theories. In constructing the series of minimal models using covariant vertex operators, we find a necessary restriction on the Cartan matrix of the Super-Lie-Algebra, also for the general case. Within this framework, this restriction claims that there be a minimum of one non-vanishing element on the diagonal of the Cartan matrix, which is without parallel in bosonic conformal field theory. As a consequence only two series of SSLA's yield minimal models, namely Osp(2n|2n-1) and Osp(2n|2n+1). Subsequently some general aspects of degenerate representations of SW-algebras, notably the fusion rules, are investigated. As an application we discuss minimal models of SW(3/2,2), which were constructed with independent methods, in this framework. Covariant formulation is used throughout this paper.

26 pages (Plain TeX), BONN-TH-94-04

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• W-symmetry in Conformal Field Theory
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• Structure constants in the N=1 superoperator algebra
• W-Algebras, New Rational Models and Completeness of the c = 1 Classification
• Fusion Algebras of Fermionic Rational Conformal Field Theories via a Generalized Verlinde Formula
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Cited by in corpus (5)

• A note on the extended superconformal algebras associated with manifolds of exceptional holonomy
• Constraints on Higher Spin CFT${}_2$
• Unitary minimal models of SW(3/2,3/2,2) superconformal algebra and manifolds of G_2 holonomy
• The Topological G2 String
• Unitary representations of SW(3/2,2) superconformal algebra