Higher-dimensional full vertex algebras and systems of conformally covariant correlation functions

We formulate a class of systems of Euclidean correlation functions for compact $d$-dimensional conformal field theories which are not necessarily unitary. We also introduce conformal $d$-vertex algebras, $d$-dimensional analogues of full vertex algebras, and prove that such an algebra is obtained from every system of conformally covariant correlation functions. Finally, for each $d\ge 2$, we construct a family of examples satisfying these axioms, corresponding to generalized free scalar fields. For $d>2$, this family contains both unitary and non-unitary examples.