Embedding Diagrams of the N=2 Superconformal Algebra under Spectral Flow

TL;DR

This paper analyzes the embedding diagrams of N=2 superconformal algebra representations at c=3, highlighting the role of spectral flow symmetry and describing subsingular vectors in non-unitary cases.

Contribution

It systematically describes the embedding diagrams and subsingular vectors of N=2 superconformal algebra representations, emphasizing spectral flow effects.

Findings

Embedding diagrams are explicitly constructed for c=3 representations.

Spectral flow symmetry largely determines the structure of these diagrams.

The action of spectral flow on characters is explicitly calculated.

Abstract

The embedding diagrams of representations of the N=2 superconformal algebra with central charge c=3 are given. Some non-unitary representations possess subsingular vectors that are systematically described. The structure of the embedding diagrams is largely defined by the spectral flow symmetry. As an additional consistency check the action of the spectral flow on the characters is calculated.