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 language | English (US) |
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Pages (from-to) | 331-351 |
Number of pages | 21 |
Journal | Bulletin of the Brazilian Mathematical Society |
Volume | 46 |
Issue number | 3 |
DOIs | |
State | Published - Sep 1 2015 |
Keywords
- Shatashvili-Vafa G superconformal algebra
- W-algebras
- free field realization
- quantum Hamiltonian reduction
ASJC Scopus subject areas
- Mathematics(all)