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

Reimundo Heluani, Lázaro O. Rodríguez Díaz*

*Corresponding author for this work

Research output: Contribution to journalArticle

3 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)331-351
Number of pages21
JournalBulletin of the Brazilian Mathematical Society
Volume46
Issue number3
DOIs
StatePublished - Sep 1 2015

Keywords

  • Shatashvili-Vafa G superconformal algebra
  • W-algebras
  • free field realization
  • quantum Hamiltonian reduction

ASJC Scopus subject areas

  • Mathematics(all)

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