Refining the elliptic genus

Abstract We show how special forms an N = 2 Landau-Ginzburg potential directly imply the presence of an N = 2 super- W algebra. If the Landau-Ginzburg model has a super- W algebra, we show how the elliptic genus can be refined so as to give much more complete information about the structure of the model. We study the super- W 3 model in some detail, and present some results and conjectures about more general models.