N=2 Current Algebras for Non-Semi-Simple Groups

TL;DR

This paper constructs N=2 superconformal algebras from N=1 non-semi-simple affine Lie algebras, revealing a central charge of c=9, which could serve as an internal space for string compactification and mirror symmetry studies.

Contribution

It introduces a novel method to build N=2 superconformal algebras from non-semi-simple Lie algebras, with specific focus on central charge properties.

Findings

Constructed N=2 superconformal algebras with central charge c=9

Showed the dependence of super Virasoro central charge on Lie algebra dimension

Proposed applications in string compactification and mirror symmetry

Abstract

We examine the problem of constructing N=2 superconformal algebras out of N=1 non-semi-simple affine Lie algebras. These N=2 superconformal theories share the property that the super Virasoro central charge depends only on the dimension of the Lie algebra. We find, in particular, a construction having a central charge c=9. This provides a possible internal space for string compactification and where mirror symmetry might be explored.