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arXiv · 1611.03487

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

Lázaro O. Rodríguez Díaz
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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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Lázaro O. Rodríguez Díaz. 2016-11-10. The $SW(3/2,2)$ superconformal algebra via a Quantum Hamiltonian Reduction of $osp(3|2)$. https://arxiv.org/abs/1611.03487

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