What controls star formation in the central 500 pc of the Galaxy?
  The star formation rate (SFR) in the Central Molecular Zone (CMZ, i.e. the
central 500 pc) of the Milky Way is lower by a factor of >10 than expected for
the substantial amount of dense gas it contains, which challenges current star
formation theories. In this paper, we quantify which physical mechanisms could
be responsible. On scales larger than the disc scale height, the low SFR is
found to be consistent with episodic star formation due to secular
instabilities or possibly variations of the gas inflow along the Galactic bar.
The CMZ is marginally Toomre-stable when including gas and stars, but highly
Toomre-stable when only accounting for the gas, indicating a low condensation
rate of self-gravitating clouds. On small scales, we find that the SFR in the
CMZ may be caused by an elevated critical density for star formation due to the
high turbulent pressure. The existence of a universal density threshold for
star formation is ruled out. The HI-H$_2$ phase transition of hydrogen, the
tidal field, a possible underproduction of massive stars due to a bottom-heavy
initial mass function, magnetic fields, and cosmic ray or radiation pressure
feedback also cannot individually explain the low SFR. We propose a
self-consistent cycle of star formation in the CMZ, in which the effects of
several different processes combine to inhibit star formation. The
rate-limiting factor is the slow evolution of the gas towards collapse - once
star formation is initiated it proceeds at a normal rate. The ubiquity of star
formation inhibitors suggests that a lowered central SFR should be a common
phenomenon in other galaxies. We discuss the implications for galactic-scale
star formation and supermassive black hole growth, and relate our results to
the star formation conditions in other extreme environments.
