Recent advances and open questions on the susy structure of the chiral de Rham Complex

Abstract

We review different constructions of the supersymmetry subalgebras of the chiral de Rham complex on special holonomy manifolds. We describe the difference between the holomorphic-anti-holomorphic sectors based on a local free ghost system vs the decomposition in left-right sectors from a local Boson-Fermion system. We describe the topological twist in the case of $G_2$ and $Spi{n}_7$ manifolds. We describe the construction of these algebras as quantum Hamiltonian reduction of Lie superalgebras at the minimal or superprincipal nilpotent.

References in corpus (4)

• Notes on the K3 Surface and the Mathieu group M_24
• G_2-manifolds and associative submanifolds via semi-Fano 3-folds
• Supersymmetric vertex algebras
• Superconformal structures on generalized Calabi-Yau metric manifolds

Cited by in corpus (1)

• Topological G${}_2$ and Spin(7) strings at 1-loop from double complexes