Singular Vectors of the Topological Conformal Algebra

TL;DR

This paper introduces a new, independent construction for topological singular vectors in the twisted N=2 superconformal algebra, establishing a link with sl(2) singular vectors and providing recursive formulas for their derivation.

Contribution

It presents a novel, algebra-independent method for constructing topological singular vectors and demonstrates an isomorphism with sl(2) singular vectors.

Findings

Provides a general recursive formula for topological singular vectors.

Establishes an isomorphism between topological and sl(2) singular vectors.

Introduces generalized Verma modules for the twisted N=2 algebra.

Abstract

A general construction is found for `topological' singular vectors of the twisted N=2 superconformal algebra. It demonstrates many parallels with the known construction for sl(2) singular vectors due to Malikov--Feigin--Fuchs, but is formulated independently of the latter. The two constructions taken together provide an isomorphism between topological and sl(2)- singular vectors. The general formula for topological singular vectors can be reformulated as a chain of direct recursion relations that allow one to derive a given singular vector |S(r,s)> from the lower ones |S(r,s'<s)>. We also introduce generalized Verma modules over the twisted N=2 algebra and show that they provide a natural setup for the new construction for topological singular vectors.