  We present the High-$z$ Evolution of Large and Luminous Objects (HELLO)
project, a set of more than 30 high-resolution hydrodynamical cosmological
simulations aimed to study Milky Way analogues ($M_\star\sim10^{10-11}$
$\mathrm{M}_\odot$) at high redshift, namely at $z=3.6$ (age $\sim$ 1.7 Gyr)
and $z=2$ (age $\sim$ 3.3 Gyr). The HELLO project features an updated scheme
for chemical enrichment and the addition of local photoionization feedback
processes. Independently of redshift and stellar mass, all galaxies follow a
similar evolutionary path: (i) first a smooth progression along the star
formation main sequence, where galaxies grow in both stellar mass and size,
(ii) a (short) period of intense star formation, which causes a contraction
phase in the stellar size, until the galaxies reach their peak star formation
rate (SFR), during this period we also witness a significant black hole growth,
and (iii) the onset of declining SFRs, which is due to a mix of gas
consumption, stellar feedback, and AGN feedback, but with AGN feedback still
being subdominant with respect to stellar feedback for energy deposition. The
exact phase in which a galaxy in our mass range can be found at a given
redshift is set by its gas reservoir and assembly history. Finally, our
galaxies are in excellent agreement with several various scaling relations
observed with the Hubble Space Telescope and the James Webb Space Telescope,
and hence can be used to provide the theoretical framework to interpret current
and future observations from these facilities and shed light on the transition
from star-forming to quiescent galaxies.
