The Even and the Odd Spectral Flows on the N=2 Superconformal Algebras

TL;DR

This paper explores the relationships between even and odd spectral flows in N=2 superconformal algebras, revealing that the odd flows are fundamental and analyzing the properties of topological spectral flows.

Contribution

It demonstrates that the even spectral flow is generated by the odd spectral flow, establishing the odd spectral flow as the fundamental transformation in the algebra.

Findings

The even spectral flow is generated by the odd spectral flow.

Thorough analysis of four topological spectral flows, with two presented for the first time.

Topological spectral flows exhibit drastically different properties from non-topological ones.

Abstract

There are two different spectral flows on the N=2 superconformal algebras (four in the case of the Topological algebra). The usual spectral flow, first considered by Schwimmer and Seiberg, is an even transformation, whereas the spectral flow previously considered by the author and Rosado is an odd transformation. We show that the even spectral flow is generated by the odd spectral flow, and therefore only the latter is fundamental. We also analyze thoroughly the four ``topological'' spectral flows, writing two of them here for the first time. Whereas the even and the odd spectral flows have quasi-mirrored properties acting on the Antiperiodic or the Periodic algebras, the topological even and odd spectral flows have drastically different properties acting on the Topological algebra. The other two topological spectral flows have mixed even and odd properties. We show that the even and the even-odd topological spectral flows are generated by the odd and the odd-even topological spectral flows, and therefore only the latter are fundamental.