  The correlation observed between monochromatic X-ray and UV luminosities in
radiatively-efficient active galactic nuclei (AGN) lacks a clear theoretical
explanation despite being used for many applications. Such a correlation, with
its small intrinsic scatter and its slope that is smaller than unity in log
space, represents the compelling evidence that a mechanism regulating the
energetic interaction between the accretion disk and the X-ray corona must be
in place. This ensures that going from fainter to brighter sources the coronal
emission increases less than the disk emission. We discuss here a
self-consistently coupled disk-corona model that can identify this regulating
mechanism in terms of modified viscosity prescriptions in the accretion disk.
The model predicts a lower fraction of accretion power dissipated in the corona
for higher accretion states. We then present a quantitative observational test
of the model using a reference sample of broad-line AGN and modeling the
disk-corona emission for each source in the $L_X-L_{UV}$ plane. We used the
slope, normalization, and scatter of the observed relation to constrain the
parameters of the theoretical model. For non-spinning black holes and static
coronae, we find that the accretion prescriptions that match the observed slope
of the $L_X-L_{UV}$ relation produce X-rays that are too weak with respect to
the normalization of the observed relation. Instead, considering
moderately-outflowing Comptonizing coronae and/or a more realistic
high-spinning black hole population significantly relax the tension between the
strength of the observed and modeled X-ray emission, while also predicting very
low intrinsic scatter in the $L_X-L_{UV}$ relation. In particular, this latter
scenario traces a known selection effect of flux-limited samples that
preferentially select high-spinning, hence brighter, sources.
