  The origin of hot Jupiters -- gas giant exoplanets orbiting very close to
their host stars -- is a long-standing puzzle. Planet formation theories
suggest that such planets are unlikely to have formed in-situ but instead may
have formed at large orbital separations beyond the snow line and migrated
inward to their present orbits. Two competing hypotheses suggest that the
planets migrated either through interaction with the protoplanetary disk during
their formation, or by disk-free mechanisms such as gravitational interactions
with a third body. Observations of eccentricities and spin-orbit misalignments
of hot Jupiter systems have been unable to differentiate between the two
hypotheses. In the present work, we suggest that chemical depletions in hot
Jupiter atmospheres might be able to constrain their migration mechanisms. We
find that sub-solar carbon and oxygen abundances in Jovian-mass hot Jupiters
around Sun-like stars are hard to explain by disk migration. Instead, such
abundances are more readily explained by giant planets forming at large orbital
separations, either by core accretion or gravitational instability, and
migrating to close-in orbits via disk-free mechanisms involving dynamical
encounters. Such planets also contain solar or super-solar C/O ratios. On the
contrary, hot Jupiters with super-solar O and C abundances can be explained by
a variety of formation-migration pathways which, however, lead to solar or
sub-solar C/O ratios. Current estimates of low oxygen abundances in hot Jupiter
atmospheres may be indicative of disk-free migration mechanisms. We discuss
open questions in this area which future studies will need to investigate.
