  In a Universe where AGN feedback regulates star formation in massive
galaxies, a strong correlation between these two quantities is expected. If the
gas causing star formation is also responsible for feeding the central black
hole, then a positive correlation is expected. If powerful AGNs are responsible
for the star formation quenching, then a negative correlation is expected.
Observations so far have mainly found a mild correlation or no correlation at
all (i.e. a flat relation between star formation rate (SFR) and AGN
luminosity), raising questions about the whole paradigm of "AGN feedback". In
this paper, we report the predictions of the GALFORM semi-analytical model,
which has a very strong coupling between AGN activity and quenching of star
formation. The predicted SFR-AGN luminosity correlation appears negative in the
low AGN luminosity regime, where AGN feedback acts, but becomes strongly
positive in the regime of the brightest AGN. Our predictions reproduce
reasonably well recent observations by Rosario et al., yet there is some
discrepancy in the normalisation of the correlation at low luminosities and
high redshifts. Though this regime could be strongly influenced by
observational biases, we argue that the disagreement could be ascribed to the
fact that GALFORM neglects AGN variability effects. Interestingly, the galaxies
that dominate the regime where the observations imply a weak correlation are
massive early-type galaxies that are subject to AGN feedback. Nevertheless,
these galaxies retain high enough molecular hydrogen contents to maintain
relatively high star formation rates and strong infrared emission.
