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 $$ \mathcal{Q} $$-curvature charge and an exponential Liouville-type potential. The theories are non-unitary and conformally invariant. https://halohealthcarers.shop/product-category/drop-foot-support/