TL;DR
This paper explores how specific Landau-Ginzburg potentials imply super-$W$ algebras and demonstrates how elliptic genus refinement reveals detailed structural information, focusing on the super-$W_3$ model.
Contribution
It establishes a connection between special Landau-Ginzburg potentials and super-$W$ algebras, and develops a refined elliptic genus framework for these models.
Findings
Super-$W_3$ model analysis provides new structural insights.
Refined elliptic genus captures more detailed model information.
Conjectures extend to more general super-$W$ models.
Abstract
We show how special forms of an Landau-Ginzburg potential directly imply the presence of an super- algebra. If the Landau-Ginzburg model has a super- 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- model in some detail, and present some results and conjectures about more general models.
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