Classification of Cohomogeneity One Strings

TL;DR

This paper classifies cohomogeneity one strings, which are strings with continuous symmetries, by analyzing Killing vector fields in Minkowski spacetime, revealing seven classes with spacelike and four with timelike symmetries.

Contribution

It provides a comprehensive classification of cohomogeneity one strings based on their symmetry properties in Minkowski spacetime.

Findings

Seven classes of spacelike symmetric strings identified.

Four classes of stationary (timelike symmetric) strings identified.

Killing vector fields are classified into equivalence classes using isometries.

Abstract

We define the cohomogeneity one string, string with continuous symmetries, as its world surface is tangent to a Killing vector field of a target space. We classify the Killing vector fields by an equivalence relation using isometries of the target space. We find that the equivalence classes of Killing vectors in Minkowski spacetime are partitioned into seven families. It is clarified that there exist seven types of strings with spacelike symmetries and four types of strings with timelike symmetries, stationary strings.