  Current models of galaxy evolution suggest that feedback from active galactic
nuclei is needed to explain the high-luminosity cutoff in the galaxy luminosity
function. Exactly how an AGN outflow couples with the ambient medium and
suppresses star formation remains poorly understood. However, we have recently
uncovered an important clue to how that coupling might work. Observations of
H-alpha emission and blue light from the universe's most luminous galaxies,
which occupy the centers of galaxy clusters, show that star formation happens
only if the minimum specific entropy of the intracluster gas is less than 30
keV cm^2. Here we suggest that this threshold for star formation is set by the
physics of electron thermal conduction, implying that conduction is critical
for channeling AGN energy input toward incipient star-forming regions and
limiting the progress of star formation.
