Chiral Determinant Formulae and Subsingular Vectors for the N=2 Superconformal Algebras

TL;DR

This paper derives conjectural determinant formulas for various N=2 superconformal algebras, analyzing singular and subsingular vectors to deepen understanding of their structure and symmetries.

Contribution

It introduces new conjectures for N=2 superconformal algebra determinant formulas and uncovers subsingular vectors through spectral flow analysis and computational checks.

Findings

Derived conjectures for N=2 algebra determinant formulas

Identified subsingular vectors in the algebras

Analyzed spectral flow symmetries and singular vectors

Abstract

We derive conjectures for the N=2 "chiral" determinant formulae of the Topological algebra, the Antiperiodic NS algebra, and the Periodic R algebra, corresponding to incomplete Verma modules built on chiral topological primaries, chiral and antichiral NS primaries, and Ramond ground states, respectively. Our method is based on the analysis of the singular vectors in chiral Verma modules and their spectral flow symmetries, together with some computer exploration and some consistency checks. In addition, and as a consequence, we uncover the existence of subsingular vectors in these algebras, giving examples (subsingular vectors are non-highest-weight null vectors which are not descendants of any highest-weight singular vectors).