  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.
