The Structure of Verma Modules over the N=2 Superconformal Algebra

TL;DR

This paper classifies the degeneration patterns of Verma modules over the N=2 superconformal algebra, providing explicit formulas for singular and subsingular vectors, and analyzing module embeddings in two-dimensional conformal field theory.

Contribution

It introduces a comprehensive classification of degeneration patterns and explicit formulas for singular and subsingular vectors in N=2 superconformal Verma modules.

Findings

Explicit formulas for singular vectors

Classification of degeneration patterns

General formulas for subsingular vectors

Abstract

We classify degeneration patterns of Verma modules over the N=2 superconformal algebra in two dimensions. Explicit formulae are given for singular vectors that generate maximal submodules in each of the degenerate cases. The mappings between Verma modules defined by these singular vectors are embeddings; in particular, their compositions never vanish. As a by-product, we also obtain general formulae for N=2 subsingular vectors.