  The LIGO-Virgo-KAGRA Collaboration has detected over one hundred compact
binary mergers in gravitational waves, but the formation history of these
binaries remains an open question. Finding the host galaxies of these mergers
will provide critical information that reveals how these binaries were formed.
However, without an electromagnetic counterpart, localizing gravitational wave
events to their hosts is challenging with the current generation of
gravitational wave detectors. Next-generation detectors will localize some
compact binary mergers to a small volume that allows for direct association
with their hosts. To demonstrate the promise these detectors hold, we simulate
a population of binary black hole and neutron star-black hole mergers using a
next-generation gravitational wave network comprised of Cosmic Explorer and
Einstein Telescope. We find that ~4% of binary black hole events within a
redshift of 0.5 and ~3% of neutron star-black hole events within a redshift of
0.3 will be localized to a volume smaller than 100 Mpc^3, the volume in which
we expect only one likely host galaxy. With the astrophysical merger rate
estimated from the LIGO-Virgo-KAGRA Collaboration's third observing run, we
expect to precisely localize one binary black hole event every eight days and
one neutron star-black hole event every 1.5 months. With three years of
gravitational wave observations (O(100) binary black hole mergers with host
associations), we will be able to distinguish whether binary black hole host
galaxies trace stellar mass or star formation rate, constraining the delay time
distribution and shedding light on the formation channels of binary black
holes.
