On the Equivalence of Affine sl(2) and N=2 Superconformal Representation Theories

TL;DR

This paper demonstrates the equivalence between the representation theories of affine sl(2) and N=2 superconformal algebras, providing a translation dictionary and analyzing module structures via extremal vector diagrams.

Contribution

It introduces a translation dictionary between sl(2) and N=2 algebras and proves their representation theories are equivalent under spectral flow transformations.

Findings

Representation theories are equivalent modulo spectral flows.

A dictionary translating key representation terms between the two algebras.

Modules' structures are characterized using extremal vector diagrams.

Abstract

There exist two different languages, the ^sl(2) and N=2 ones, to describe similar structures; a dictionary is given translating the key representation-theoretic terms related to the two algebras. The main tool to describe the structure of ^sl(2) and N=2 modules is provided by diagrams of extremal vectors. The ^sl(2) and N=2 representation theories of certain highest-weight types turn out to be equivalent modulo the respective spectral flows.