### Abstract

We review the Liouville theory calculation of the genus-one path integral for c ≤ 1 conformal models coupled to two-dimensional gravity. From the modular integrand we derive the existence of an infinite number of physical operators which are in one-to-one correspondence with the conformal primary fields and null states of the matter theory. We also calculate the torus path integral and find the spectrum of physical operators for c ̂ ≤ 1 superconformal models coupled to supergravity. The amplitude in the odd spin structure requires a special treatment and is found to be proportional to the Witten index of the matter theory.

Original language | English (US) |
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Pages (from-to) | 559-585 |

Number of pages | 27 |

Journal | Nuclear Physics, Section B |

Volume | 360 |

Issue number | 2-3 |

DOIs | |

State | Published - Aug 19 1991 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

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## Cite this

Bershadsky, M., & Klebanov, I. R. (1991). Partition functions and physical states in two-dimensional quantum gravity and supergravity.

*Nuclear Physics, Section B*,*360*(2-3), 559-585. https://doi.org/10.1016/0550-3213(91)90416-U