The Refined Elliptic Genus and Coulomb Gas Formulations of $N=2$ Superconformal Coset Models

TL;DR

This paper explores various Coulomb gas formulations of N=2 superconformal coset models, linking them to Landau-Ginzburg structures to refine elliptic genus computations and analyze model characters.

Contribution

It introduces multiple Coulomb gas formulations and mappings for N=2 superconformal coset models, enhancing the extraction of detailed character information.

Findings

Multiple Coulomb gas formulations established

Mappings between different formulations provided

Refined elliptic genus computation methods developed

Abstract

We describe, in some detail, a number of different Coulomb gas formulations of $N=2$ superconformal coset models. We also give the mappings between these formulations. The ultimate purpose of this is to show how the Landau-Ginzburg structure of these models can be used to extract the $W$-generators, and to show how the computation of the elliptic genus can be refined so as to extract very detailed information about the characters of component parts of the model.