Alternate notions of N=1 superconformality and deformations of N=1 vertex superalgebras

We consider alternate notions of N=1 superconformality arising from scaling the odd (fermionic) variable by an even parameter. We show that this naturally gives rise to the notion of deformed N=1 vertex superalgebra. We formulate this notion using a Jacobi identity with odd formal variables in which one of a continuous family of deformed N=1 superconformal shifts is incorporated into the usual Jacobi identity for vertex superalgebras. This shift in the Jacobi identity dictates the form of the odd formal variable components of the vertex operators, and naturally gives rise to a representation of the Lie superalgebra isomorphic to the two-dimensional algebra. of supercierivations with basis consisting of the usual conformal operator and the deformed N=1 superconformal operator.