## Abstract

We consider a generalization of the two-dimensional Liouville conformal field theory to any number of even dimensions. The theories consist of a log-correlated scalar field with a background Q-curvature charge and an exponential Liouville-type potential. The theories are non-unitary and conformally invariant. They localize semiclassically on solutions that describe manifolds with a constant negative Q-curvature. We show that C _{T} is independent of the Q-curvature charge and is the same as that of a higher derivative scalar theory. We calculate the A-type Euler conformal anomaly of these theories. We study the correlation functions, derive an integral expression for them and calculate the three-point functions of light primary operators. The result is a higher-dimensional generalization of the two-dimensional DOZZ formula for the three-point function of such operators.

Original language | English |
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Article number | 119 |

Journal | Journal of High Energy Physics |

Volume | 2018 |

Issue number | 6 |

DOIs | |

State | Published - 2018 |

## Keywords

- Anomalies in Field and String Theories
- Conformal Field Theory
- Field Theories in Higher Dimensions