EXTENDED SUPERCONFORMAL SYMMETRY, FREUDENTHAL TRIPLE SYSTEMS AND GAUGED WZW MODELS

TL;DR

This paper reviews the construction of extended superconformal algebras over triple systems, especially Freudenthal systems, and classifies gauged WZW models with N=4 superconformal symmetry, advancing understanding of their algebraic structures.

Contribution

It provides a detailed classification of N=2 and N=4 superconformal algebras over Freudenthal triple systems and analyzes gauged WZW models with N=4 symmetry.

Findings

Extended N=2 superconformal algebras over Freudenthal triple systems.

Extension to maximal N=4 superconformal algebras with specific symmetry.

Classification of gauged WZW models with N=4 superconformal symmetry.

Abstract

We review the construction of extended ( N=2 and N=4 ) superconformal algebras over triple systems and the gauged WZW models invariant under them. The N=2 superconformal algebras (SCA) realized over Freudenthal triple systems (FTS) admit extension to ``maximal'' N=4 SCA's with SU(2)XSU(2)XU(1) symmetry. A detailed study of the construction and classification of N=2 and N=4 SCA's over Freudenthal triple systems is given. We conclude with a study and classification of gauged WZW models with N=4 superconformal symmetry.