Spectral Flows and Twisted Topological Theories

TL;DR

This paper studies how spectral flows act on N=2 twisted topological theories, revealing their role in mapping between theories, automorphisms of topological algebra, and simplifying null vector computations, with specific results at level 2.

Contribution

It demonstrates that spectral flows serve as a topological algebra automorphism, providing a new method to relate and analyze twisted topological theories.

Findings

Spectral flows map null vectors to null vectors, simplifying their computation.

Explicit level 2 results for spectral flow actions.

Discussion of spectral flow in DDK and KM realizations.

Abstract

We analyze the action of the spectral flows on N=2 twisted topological theories. We show that they provide a useful mapping between the two twisted topological theories associated to a given N=2 superconformal theory. This mapping can also be viewed as a topological algebra automorphism. In particular null vectors are mapped into null vectors, considerably simplifying their computation. We give the level 2 results. Finally we discuss the spectral flow mapping in the case of the DDK and KM realizations of the topological algebra.