  We report the formation of bound star clusters in a sample of high-resolution
cosmological zoom-in simulations of z>5 galaxies from the FIRE project. We find
that bound clusters preferentially form in high-pressure clouds with gas
surface densities over 10^4 Msun pc^-2, where the cloud-scale star formation
efficiency is near unity and young stars born in these regions are
gravitationally bound at birth. These high-pressure clouds are compressed by
feedback-driven winds and/or collisions of smaller clouds/gas streams in highly
gas-rich, turbulent environments. The newly formed clusters follow a power-law
mass function of dN/dM~M^-2. The cluster formation efficiency is similar across
galaxies with stellar masses of ~10^7-10^10 Msun at z>5. The age spread of
cluster stars is typically a few Myrs and increases with cluster mass. The
metallicity dispersion of cluster members is ~0.08 dex in [Z/H] and does not
depend on cluster mass significantly. Our findings support the scenario that
present-day old globular clusters (GCs) were formed during relatively normal
star formation in high-redshift galaxies. Simulations with a stricter/looser
star formation model form a factor of a few more/fewer bound clusters per
stellar mass formed, while the shape of the mass function is unchanged.
Simulations with a lower local star formation efficiency form more stars in
bound clusters. The simulated clusters are larger than observed GCs due to
finite resolution. Our simulations are among the first cosmological simulations
that form bound clusters self-consistently in a wide range of high-redshift
galaxies.
