Li filtrations of SUSY vertex algebras

Any vertex algebra has a canonical decreasing filtration, called the 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 for supersymmetric vertex algebras. We prove that the associated graded superspace of our filtration has a structure of a SUSY vertex Poisson algebra. We also introduce and discuss related notions, such as Zhu’s C2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_2$$\end{document}-Poisson superalgebras, associated superschemes, and singular supports, for SUSY vertex algebras.