The Other Spectral Flow

TL;DR

This paper introduces a new type of spectral flow in N=2 superconformal algebra that preserves chiral and antichiral rings, differing from the conventional spectral flow, with implications for null states and algebra automorphisms.

Contribution

It identifies and analyzes a novel spectral flow on the untwisted N=2 superconformal algebra, distinct from the standard one, and explores its properties and effects.

Findings

The new spectral flow maps chiral to chiral and antichiral to antichiral states.

It differs from the usual spectral flow in its action on the algebra and states.

The paper discusses the automorphism and null state transformations under this flow.

Abstract

Recently we showed that the spectral flow acting on the N=2 twisted topological theories gives rise to a topological algebra automorphism. Here we point out that the untwisting of that automorphism leads to a spectral flow on the untwisted N=2 superconformal algebra which is different from the usual one. This "other" spectral flow does not interpolate between the chiral ring and the antichiral ring. In particular, it maps the chiral ring into the chiral ring and the antichiral ring into the antichiral ring. We discuss the similarities and differences between both spectral flows. We also analyze their action on null states.