### Abstract

A classical string whose world sheet shares a one-dimensional symmetry with the spacetime is called cohomogeneity-one (C1). We propose C1-string integrability, i.e. integrability of all C1 strings in the spacetime, as a class of hidden symmetry of a spacetime. The C1 string may probe symmetry which is not probed by a particle. We present a simple, systematic procedure for finding constants of motion of a C1 string and examining C1 string integrability of a spacetime. We apply the framework to some physically important spacetimes such as AdS_{5}, AdS_{5} × S^{5}, and AdS_{5} × T^{p,q}. C1 strings and C1-string integrability may be useful for a prior examination of general string integrability of a highly symmetric spacetime since, among the examples above, all C1 string integrable spacetimes are string-integrable, and the previously obtained chaotic string solutions in those or other spacetimes are of class C1.

Original language | English |
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Article number | 155009 |

Journal | Classical and Quantum Gravity |

Volume | 36 |

Issue number | 15 |

DOIs | |

Publication status | Published - 2019 Jul 17 |

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### Keywords

- Hamiltonian system
- hidden symmetry
- pacetime symmetry

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Classical and Quantum Gravity*,

*36*(15), [155009]. https://doi.org/10.1088/1361-6382/ab2e28