The Shatashvili-Vafa $G_2$ superconformal algebra as a Quantum Hamiltonian Reduction of $D(2,1;\alpha )$

Reimundo Heluani, Lázaro O. Rodríguez Díaz

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 r…