  We investigate the clustering and halo properties of $\sim 5000$
Ly$\alpha$-selected emission line galaxies (LAEs) from the Slicing COSMOS 4K
(SC4K) and from archival NB497 imaging of SA22 split in 15 discrete redshift
slices between $z \sim 2.5 - 6$. We measure clustering lengths of $r_0 \sim 3 -
6\ h^{-1}$ Mpc and typical halo masses of $\sim 10^{11}$ M$_\odot$ for our
narrowband-selected LAEs with typical $L_{\rm{Ly}\alpha} \sim 10^{42 - 43}$ erg
s$^{-1}$. The intermediate band-selected LAEs are observed to have $r_0 \sim
3.5 - 15\ h^{-1}$ Mpc with typical halo masses of $\sim 10^{11 - 12}$ M$_\odot$
and typical $L_{\rm{Ly}\alpha} \sim 10^{43 - 43.6}$ erg s$^{-1}$. We find a
strong, redshift-independent correlation between halo mass and Ly$\alpha$
luminosity normalized by the characteristic Ly$\alpha$ luminosity,
$L^\star(z)$. The faintest LAEs ($L \sim 0.1\ L^\star(z)$) typically identified
by deep narrowband surveys are found in $10^{10}$ M$_\odot$ halos and the
brightest LAEs ($L \sim 7\ L^\star(z)$) are found in $\sim 5 \times 10^{12}$
M$_\odot$ halos. A dependency on the rest-frame 1500 \AA~UV luminosity,
M$_\rm{UV}$, is also observed where the halo masses increase from $10^{11}$ to
$10^{13}$ M$_\odot$ for M$_\rm{UV} \sim -19$ to $-23.5$ mag. Halo mass is also
observed to increase from $10^{9.8}$ to $10^{12.3}$ M$_\odot$ for
dust-corrected UV star formation rates from $\sim 0.6$ to $10$ M$_\odot$
yr$^{-1}$ and continues to increase up to $10^{13.5}$ M$_\odot$ in halo mass,
where the majority of those sources are AGN. All the trends we observe are
found to be redshift-independent. Our results reveal that LAEs are the likely
progenitors of a wide range of galaxies depending on their luminosity, from
dwarf-like, to Milky Way-type, to bright cluster galaxies. LAEs therefore
provide unique insight into the early formation and evolution of the galaxies
we observe in the local Universe.
