The Shatashvili-Vafa G 2 superconformal algebra as a quantum Hamiltonian reduction of D(2, 1; α)

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• 作者：Reimundo Heluani ; Lázaro O. Rodríguez Díaz
• 关键词：Shatashvili ; Vafa G 2 superconformal algebra ; quantum Hamiltonian reduction ; W ; algebras ; free field realization ; 17B69 ; 17B68 ; 81R10
• 刊名：Bulletin of the Brazilian Mathematical Society
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：46
• 期：3
• 页码：331-351
• 全文大小：216 KB
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• 作者单位：Reimundo Heluani (1)
  Lázaro O. Rodríguez Díaz (1)
  
  1. IMPA, Estrada Dona Castorina, 110 Jardim Botanico, 22460-320, Rio de Janeiro, RJ, Brazil
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Mathematical and Computational Physics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1678-7714

文摘

We obtain the superconformal algebra associated to a sigma model with target a manifold with G ₂ holonomy, i.e., the Shatashvili-Vafa G ₂ algebra as a quantum Hamiltonian reduction of the exceptional Lie superalgebra D(2, 1; α) for α = 1. We produce the complete family of W-algebras SW (3/2, 3/2, 2) (extensions of the N = 1 superconformal algebra by two primary supercurrents of conformal weight 3/2 and 2 respectively) as a quantum Hamiltonian reduction of D(2, 1; α). As a corollary we find a free field realization of the Shatashvili-Vafa G ₂ algebra, and an explicit description of the screening operators. Keywords Shatashvili-Vafa G ₂ superconformal algebra quantum Hamiltonian reduction W-algebras free field realization