### Abstract

We give a formulation of two-dimensional topological gravity without matter in terms of a supersymmetric conformally invariant field theory and derive a path integral expression for the physical amplitudes. A careful analysis of the contact terms of the physical operators reveals the presence of a non-commutative algebra, isomorphic to the Virasoro algebra. We show that this algebra completely determines all the amplitudes at arbitrary genus, which coincide with those of the one-matrix model at the k = 1 critical point.

Original language | English (US) |
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Pages (from-to) | 457-489 |

Number of pages | 33 |

Journal | Nuclear Physics, Section B |

Volume | 348 |

Issue number | 3 |

DOIs | |

State | Published - Jan 21 1991 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

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## Cite this

Verlinde, E., & Verlinde, H. (1991). A solution of two-dimensional topological quantum gravity.

*Nuclear Physics, Section B*,*348*(3), 457-489. https://doi.org/10.1016/0550-3213(91)90200-H