Cohomogeneity-one-string integrability of spacetimes

TL;DR

This paper develops a framework to reduce cohomogeneity-one strings in various spacetimes to mechanical systems and analyzes their integrability, potentially uncovering new hidden symmetries.

Contribution

It introduces a general method for studying the integrability of symmetric string configurations in diverse spacetimes.

Findings

Cohomogeneity-one strings in AdS_5 are analyzed for integrability.

The method clarifies integrability status in AdS_5 x S^5 and AdS_5 x T^{p,q}.

Potential discovery of new hidden symmetries in spacetimes.

Abstract

We present a framework for reducing all possible cohomogeneity-one strings, i.e., strings with geometrical symmetry, in a given spacetime to mechanical systems, and for analyzing integrability of the systems. As applications, it is clarified whether the systems of cohomogeneity-one strings in $AdS_5$, $AdS_5 \times S^5$, and $AdS_5 \times T^{p,q}$ are integrable or not. This method may reveal a different type of hidden symmetry of spacetimes.