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 \( \mathcal{Q} \)-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 \( \mathcal{Q} \)-curvature. We show that C T is independent of the \( \mathcal{Q} \)-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.
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Levy, T., Oz, Y. Liouville conformal field theories in higher dimensions. J. High Energ. Phys. 2018, 119 (2018). https://doi.org/10.1007/JHEP06(2018)119
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DOI: https://doi.org/10.1007/JHEP06(2018)119