The Shatashvili-Vafa G₂ superconformal algebra as a Quantum Hamiltonian Reduction of D(2,1;α)

2014/06/18 by Reimundo Heluani, Lázaro O. Rodríguez Díaz, Heluani, Reimundo +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1406.4808

openalex publication_date 2014/06/18 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We obtain the superconformal algebra associated to a sigma model with target a manifold with G₂ holonomy, i.e., the Shatashvili-Vafa G₂ 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 G₂ algebra, and an explicit description of the screening operators.

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