  Negative feedback from active galactic nuclei (AGN) is considered a key
mechanism in shaping galaxy evolution. Fast, extended outflows are frequently
detected in the AGN host galaxies at all redshifts and luminosities, both in
ionised and molecular gas. However, these outflows are only "potentially" able
to quench star formation and we are still missing a decisive evidence of
negative feedback in action. Here we present Spectrograph for INtegral Field
Observations in the Near Infrared (SINFONI) H- and K-band integral-field
spectroscopic observations of two quasars at $z\sim$2.4 characterised by fast,
extended outflows detected through the [OIII]$\lambda$5007 line (Carniani et
al. 2015). The high signal-to-noise ratio of our observations allows us to
identify faint narrow (FWHM $< 500$ km/s), and spatially extended components in
[OIII]$\lambda$5007 and H$\alpha$ emission associated with star formation in
the host galaxy. Such star-formation powered emission is spatially
anti-correlated with the fast outflows. The ionised outflows therefore appear
to be able to suppress star formation in the region where the outflow is
expanding. However the detection of narrow, spatially-extended H$\alpha$
emission indicates star formation rates of at least $\sim 50-90$
M$_{\odot}$/yr, suggesting either that AGN feedback does not affect the whole
galaxy or that many feedback episodes are required before star formation is
completely quenched. On the other hand, the narrow H$\alpha$ emission extending
along the edges of the outflow cone may lead also to a positive feedback
interpretation. Our results highlight the possible twofold role of galaxy-wide
outflows in host galaxy evolution.
