Liouville Conformal Field Theories in Higher Dimensions

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.

arXiv comment20 pages; Text modified, references added. Published version

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• Q-curvature and Path Integral Complexity
• $\mathcal{N}=1$ Liouville SCFT in Four Dimensions
• Boundaries in Free Higher Derivative Conformal Field Theories
• $Q$-curvature and gravity
• Conformal Invariance and Multifractality at Anderson Transitions in Arbitrary Dimensions
• Chaotic RG Flow in Tensor Models
• Odd Dimensional Nonlocal Liouville Conformal Field Theories
• Liouville Conformal Field Theory on even-dimensional spheres
• On the S-matrix of Liouville theory
• On some Coulomb gas integrals in higher dimensions
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