### Abstract

We study the integrability of the equations of motion for the Nambu-Goto strings with a cohomogeneity-one symmetry in Minkowski spacetime. A cohomogeneity-one string has a world surface which is tangent to a Killing vector field. By virtue of the Killing vector, the equations of motion reduce to the geodesic equation in the orbit space. Cohomogeneity-one strings are classified into seven classes (types I to VII). We investigate the integrability of the geodesic equations for all the classes and find that the geodesic equations are integrable. For types I to VI, the integrability comes from the existence of Killing vectors on the orbit space which are the projections of Killing vectors on Minkowski spacetime. For type VII, the integrability is related to a projected Killing vector and a nontrivial Killing tensor on the orbit space. We also find that the geodesic equations of all types are exactly solvable, and show the solutions.

Original language | English |
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Article number | 105006 |

Journal | Classical and Quantum Gravity |

Volume | 27 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2010 |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Classical and Quantum Gravity*,

*27*(10), [105006]. https://doi.org/10.1088/0264-9381/27/10/105006

**Exactly solvable strings in Minkowski spacetime.** / Kozaki, Hiroshi; Koike, Tatsuhiko; Ishihara, Hideki.

Research output: Contribution to journal › Article

*Classical and Quantum Gravity*, vol. 27, no. 10, 105006. https://doi.org/10.1088/0264-9381/27/10/105006

}

TY - JOUR

T1 - Exactly solvable strings in Minkowski spacetime

AU - Kozaki, Hiroshi

AU - Koike, Tatsuhiko

AU - Ishihara, Hideki

PY - 2010

Y1 - 2010

N2 - We study the integrability of the equations of motion for the Nambu-Goto strings with a cohomogeneity-one symmetry in Minkowski spacetime. A cohomogeneity-one string has a world surface which is tangent to a Killing vector field. By virtue of the Killing vector, the equations of motion reduce to the geodesic equation in the orbit space. Cohomogeneity-one strings are classified into seven classes (types I to VII). We investigate the integrability of the geodesic equations for all the classes and find that the geodesic equations are integrable. For types I to VI, the integrability comes from the existence of Killing vectors on the orbit space which are the projections of Killing vectors on Minkowski spacetime. For type VII, the integrability is related to a projected Killing vector and a nontrivial Killing tensor on the orbit space. We also find that the geodesic equations of all types are exactly solvable, and show the solutions.

AB - We study the integrability of the equations of motion for the Nambu-Goto strings with a cohomogeneity-one symmetry in Minkowski spacetime. A cohomogeneity-one string has a world surface which is tangent to a Killing vector field. By virtue of the Killing vector, the equations of motion reduce to the geodesic equation in the orbit space. Cohomogeneity-one strings are classified into seven classes (types I to VII). We investigate the integrability of the geodesic equations for all the classes and find that the geodesic equations are integrable. For types I to VI, the integrability comes from the existence of Killing vectors on the orbit space which are the projections of Killing vectors on Minkowski spacetime. For type VII, the integrability is related to a projected Killing vector and a nontrivial Killing tensor on the orbit space. We also find that the geodesic equations of all types are exactly solvable, and show the solutions.

UR - http://www.scopus.com/inward/record.url?scp=77951583512&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951583512&partnerID=8YFLogxK

U2 - 10.1088/0264-9381/27/10/105006

DO - 10.1088/0264-9381/27/10/105006

M3 - Article

AN - SCOPUS:77951583512

VL - 27

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 10

M1 - 105006

ER -