## Abstract

We consider a ĉ ≤ 1 model in the fermionic black hole background. For this purpose we consider a model which contains both the N ≤ 1 and the N ≤ 2 super-Liouville interactions. We propose that this model is dual to a recently proposed type 0A matrix quantum mechanics model with vortex deformations. We support our conjecture by showing that non-perturbative corrections to the free energy computed by both the matrix model and the super-Liouville theories agree exactly by treating the N ≤ 2 interaction as a small perturbation. We also show that a two-point function on sphere calculated from the deformed type 0A matrix model is consistent with that of the N ≤ 2 super-Liouville theory when the N ≤ 1 interaction becomes small. This duality between the matrix model and super-Liouville theories leads to a conjecture for arbitrary n-point correlation functions of the N ≤ 1 super-Liouville theory on the sphere.

Original language | English |
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Pages (from-to) | 3153-3170 |

Number of pages | 18 |

Journal | Journal of High Energy Physics |

Issue number | 1 |

DOIs | |

State | Published - 2006 |

## Keywords

- Conformal Field Models in String Theory
- Matrix Models