  We report the discovery of a 3 kpc disk of few 10^9 Ms of dense, warm H_2 in
the nearby radio galaxy 3C326 N, which shows no signs of on-going or recent
star formation and falls a factor 60 below the Schmidt-Kennicutt law.
VLT/SINFONI imaging spectroscopy shows broad (FWHM \sim 500 km/s)
ro-vibrational H_2 lines across all of the disk, with irregular profiles and
line ratios consistent with shocks. The ratio of turbulent and gravitational
energy suggests that the gas is highly turbulent and not gravitationally bound.
In absence of the driving by the jet, short turbulent dissipation times suggest
the gas should collapse rapidly and form stars, at odds with the recent
star-formation history. Motivated by hydrodynamic models of rapid H_2 formation
boosted by turbulent compression, we propose that the molecules formed from
diffuse atomic gas in the turbulent jet cocoon. Since the gas is not
self-gravitating, it cannot form molecular clouds or stars while the jet is
active, and is likely to disperse and become atomic again after the nuclear
activity ceases. We speculate that very low star-formation rates are to be
expected under such conditions, provided that the large-scale turbulence sets
the gas dynamics in molecular clouds. Our results illustrate that jets may
create large molecular reservoirs as expected in 'positive feedback' scenarios
of AGN-triggered star formation, but that this alone is not sufficient to
trigger star formation.
