Unitary minimal models of SW(3/2,3/2,2) superconformal algebra and manifolds of G_2 holonomy

Abstract

The SW(3/2,3/2,2) superconformal algebra is a W algebra with two free parameters. It consists of 3 superconformal currents of spins 3/2, 3/2 and 2. The algebra is proved to be the symmetry algebra of the coset (su(2)+su(2)+su(2))/su(2). At the central charge c=21/2 the algebra coincides with the superconformal algebra associated to manifolds of G_2 holonomy. The unitary minimal models of the SW(3/2,3/2,2) algebra and their fusion structure are found. The spectrum of unitary representations of the G_2 holonomy algebra is obtained.

34 pages, 2 figures, latex; v2: added examples in appendix D; v3: published version, corrected typos

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• Superconformal algebras for twisted connected sums and $G_2$ mirror symmetry
• Comments on M Theory Dynamics on G2 Holonomy Manifolds
• A Realization of N=1 $\mathcal{S}\mathcal{W}(3/2,2)$ Algebras with Wolf Spaces
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