Liouville Conformal Field Theories in Higher Dimensions

Understand

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.