  We investigate the sensitivity of the $\Lambda$ directed flow to the
$\Lambda$ potential in mid-central Au + Au collisions at
$\sqrt{s_{NN}}\approx3.0$--$30$ GeV. The $\Lambda$ potential obtained from the
chiral effective field theory ($\chi$EFT) is used in a microscopic transport
model, a vector version of relativistic quantum molecular dynamics (RQMDv). We
find that the density-dependent $\Lambda$ potentials, obtained from the
$\chi$EFT assuming weak momentum dependence of the potential, reproduce the
rapidity and the beam-energy dependence of the $\Lambda$ directed flow measured
by the STAR collaboration in the Beam Energy Scan program. Although the
$\Lambda$ directed flow is insensitive to the density dependence of the
potential, it is susceptible to the momentum dependence. We also show that a
hydrodynamics picture based on the blast-wave model predicts a similarity of
the proton, $\Lambda$, and $\Xi$ directed flows, but the directed flow of
$\Omega$ baryons slightly deviates from other baryons. We also show that the
quark coalescence predicts different rapidity dependence of the directed flows
for hyperons. These investigations suggest that measurements of a wide range of
the rapidity dependence of the directed flow of hyperons may provide important
information about the properties of hot and dense matter created in high-energy
heavy-ion collisions.
