The SW(3/2,2) superconformal algebra via a Quantum Hamiltonian Reduction of osp(3|2)

2016/11/10 by Díaz, Lázaro O. Rodríguez
#FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1611.03487

Abstract

We prove that the family of non-linear W-algebras SW(3/2,2) which are extensions of the N=1 superconformal algebra by a primary supercurrent of conformal weight 2 can be realized as a quantum Hamiltonian reduction of the Lie superalgebra osp(3|2). In consequence we obtain an explicit free field realization of the algebra in terms of the screening operators. At central charge c=12 the SW(3/2,2) superconformal algebra corresponds to the superconformal algebra associated to sigma models based on eight-dimensional manifolds with special holonomy Spin(7), i.e., the Shatashvili-Vafa Spin(7) superconformal algebra.

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