The Notion of N=1 Supergeometric Vertex Operator Superalgebra and the Isomorphism Theorem

Abstract

We introduce the notion of N=1supergeometric vertex operator superalgebra motivated by the geometry underlying genus-zero, two-dimensional, holomorphic N=1 superconformal field theory. We then show, assuming the convergence of certain projective factors, that the category of such objects is isomorphic to the category of N=1 Neveu–Schwarz vertex operator superalgebras.