We report the formation of bound star clusters in a sample of high-resolution cosmological zoom-in simulations of z \geq 5 galaxies from the FIRE project .
We find that bound clusters preferentially form in high-pressure clouds with gas surface densities over 10 ^ { 4 } M _ { \sun } { 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 { d } N / { d } M \sim M ^ { -2 } .
The cluster formation efficiency is similar across galaxies with stellar masses of \sim 10 ^ { 7 } – 10 ^ { 10 } M _ { \sun } at z \geq 5 .
The age spread of cluster stars is typically a few Myrs and increases with cluster mass .
The metallicity dispersion of cluster members is \sim 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 .