Li filtrations of SUSY vertex algebras

Abstract

Any vertex algebra has a canonical decreasing filtration, called Li filtration, whose associated graded space has a natural structure of a vertex Poisson algebra. In this note, we introduce an analogous filtration for any SUSY vertex algebra, which was introduced by Heluani and Kac as a superfield formalism of a supersymmetric vertex algebra. We prove that the associated graded superspace of our filtration has a structure of SUSY vertex Poisson algebras. We also introduce and discuss related notions, such as Zhu's $C_2$-Poisson superalgebras, associated superschemes and singular supports, for SUSY vertex algebras.

44 pages

References in corpus (2)

• Jets via Hasse-Schmidt Derivations
• Supersymmetric vertex algebras