Simulating Star Clusters Across Cosmic Time: I. Initial Mass Function,
  Star Formation Rates and Efficiencies
  We present radiation-magneto-hydrodynamic simulations of star formation in
self-gravitating, turbulent molecular clouds, modeling the formation of
individual massive stars, including their UV radiation feedback. The set of
simulations have cloud masses between $m_{\rm gas}=10^3$~M$_\odot$ to $3 \times
10^5$~M$_\odot$ and gas densities typical of clouds in the local universe
($\overline n_{\rm gas} \sim 1.8\times 10^2$~cm$^{-3}$) and 10$\times$ and
100$\times$ denser, expected to exist in high-redshift galaxies. The main
results are: {\it i}) The observed Salpeter power-law slope and normalisation
of the stellar initial mass function at the high-mass end can be reproduced if
we assume that each star-forming gas clump (sink particle) fragments into stars
producing on average a maximum stellar mass about $40\%$ of the mass of the
sink particle, while the remaining $60\%$ is distributed into smaller mass
stars. Assuming that the sinks fragment according to a power-law mass function
flatter than Salpeter, with log-slope $0.8$, satisfy this empirical
prescription. {\it ii}) The star formation law that best describes our set of
simulation is $d\rho_*/dt \propto \rho_{gas}^{1.5}$ if $\overline
n_{gas}<n_{cri}\approx 10^3$~cm$^{-3}$, and $d\rho_*/dt \propto \rho_{\rm
gas}^{2.5}$ otherwise. The duration of the star formation episode is roughly
$6$ cloud's sound crossing times (with $c_s=10$~km/s). {\it iii}) The total
star formation efficiency in the cloud is $f_*=2\% (m_{\rm
gas}/10^4~M_\odot)^{0.4}(1+\overline n_{\rm gas}/n_{\rm cri})^{0.91}$, for gas
at solar metallicity, while for metallicity $Z<0.1$~Z$_\odot$, based on our
limited sample, $f_*$ is reduced by a factor of $\sim 5$. {\it iv)} The most
compact and massive clouds appear to form globular cluster progenitors, in the
sense that star clusters remain gravitationally bound after the gas has been
expelled.
