  Within finite-density QCD sum-rule approach we investigate the self-energies
of $\Sigma$ hyperons propagating in nuclear matter from a correlator of
$\Sigma$ interpolating fields evaluated in the nuclear matter ground state. We
find that the Lorentz vector self-energy of the $\Sigma$ is similar to the
nucleon vector self-energy. The magnitude of Lorentz scalar self-energy of the
$\Sigma$ is also close to the corresponding value for nucleon; however, this
prediction is sensitive to the strangeness content of the nucleon and to the
assumed density dependence of certain four-quark condensate. The scalar and
vector self-energies tend to cancel, but not completely. The implications for
the couplings of $\Sigma$ to the scalar and vector mesons in nuclear matter and
for the $\Sigma$ spin-orbit force in a finite nucleus are discussed.
