### Abstract

The role of the non-singlet sector of the matrix model representation of c = 1 matter coupled to two-dimensional quantum gravity is studied in the case where the target space is a circle of finite radius. It is argued that this sector decouples for large enough radius, since the non-singlet state energies are logarithmically divergent in the double scaling limit that reproduces continuum surfaces. We identify the degrees of freedom described by this sector as vortices on the world-sheet, which are dynamically irrelevant for large radius (low temperature) but condense at a critical value of the radius, giving rise to a Kosterlitz-Thouless phase transition.

Original language | English (US) |
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Pages (from-to) | 459-474 |

Number of pages | 16 |

Journal | Nuclear Physics, Section B |

Volume | 354 |

Issue number | 2-3 |

DOIs | |

State | Published - May 6 1991 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

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## Cite this

Gross, D. J., & Klebanov, I. R. (1991). Vortices and the non-singlet sector of the c = 1 matrix model.

*Nuclear Physics, Section B*,*354*(2-3), 459-474. https://doi.org/10.1016/0550-3213(91)90363-3