### Abstract

We discuss random matrix-model representations of D = 1 string theory, with particular emphasis on the case in which the target space is a circle of finite radius. The duality properties of discretized strings are analyzed and shown to depend on the dynamics of vortices. In the representation in terms of a continuous circle of matrices we find an exact expression for the free energy, neglecting non-singlet states, as a function of the string coupling and the radius which exhibits exact duality. In a second version, based on a discrete chain of matrices, we find that vortices induce, for a finite radius, a Kosterlitz-Thouless phase transition that takes us to a c = 0 theory.

Original language | English (US) |
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Pages (from-to) | 475-498 |

Number of pages | 24 |

Journal | Nuclear Physics, Section B |

Volume | 344 |

Issue number | 3 |

DOIs | |

State | Published - Nov 19 1990 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

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## Cite this

*Nuclear Physics, Section B*,

*344*(3), 475-498. https://doi.org/10.1016/0550-3213(90)90667-3