  We study correlation functions in five-dimensional non-Lorentzian theories
with an $SU(1,3)$ conformal symmetry. Examples of such theories have recently
been obtained as $\Omega$-deformed Yang-Mills Lagrangians arising from a null
reduction of six-dimensional superconformal field theories on a conformally
compactified Minkowski space. The correlators exhibit a rich structure with
many novel properties compared to conventional correlators in Lorentzian
conformal field theories. Moreover, identifying the instanton number with the
Fourier mode number of the dimensional reduction offers a hope to formulate
six-dimensional conformal field theories in terms of five-dimensional
Lagrangian theories. To this end we show that the Fourier decompositions of
six-dimensional correlation functions solve the Ward identities of the the
$SU(1,3)$ symmetry, although more general solutions are possible. Conversely we
illustrate how one can reconstruct six-dimensional correlation functions from
those of a five-dimensional theory, and do so explicitly at 2- and 3-points. We
also show that, in a suitable decompactification limit $\Omega\to 0$, the
correlation functions become those of the DLCQ description.
