Transmutations between Singular and Subsingular Vectors of the N=2 Superconformal Algebras

TL;DR

This paper explores the structure of subsingular vectors in N=2 superconformal algebras, revealing how certain singular vectors transform under algebraic operations and expanding understanding of their representations.

Contribution

It identifies new classes of subsingular vectors in N=2 superconformal algebras and details their transformations under topological untwistings and spectral flows.

Findings

Identification of subsingular vectors beyond previously known cases

Transformation of singular vectors under topological untwisting and spectral flow

Explicit construction of vectors at levels 1 and 2

Abstract

We present subsingular vectors of the N=2 superconformal algebras other than the ones which become singular in chiral Verma modules, reported recently by Gato-Rivera and Rosado. We show that two large classes of singular vectors of the Topological algebra become subsingular vectors of the Antiperiodic NS algebra under the topological untwistings. These classes consist of BRST- invariant singular vectors with relative charges $q=-2,-1$ and zero conformal weight, and no-label singular vectors with $q=0,-1$. In turn the resulting NS subsingular vectors are transformed by the spectral flows into subsingular and singular vectors of the Periodic R algebra. We write down these singular and subsingular vectors starting from the topological singular vectors at levels 1 and 2.