  We study the separability of the Dirac equation for the four-dimensional STU
black hole space-time. In particular, we analyze in detail the separability
conditions in the pair-wise equal charge STU black hole space-time
\cite{Cvetic_PRD96}. While in the latter case the minimally coupled Dirac
equation is not separable the introduction of a specific torsion term ensures
the separability. The source of the torsion is the Kalb-Ramond field, which is
an integral part of String Theory, but further aspects of its properties and
coupling to fermionic fields remain to be studied. To derive the torsion two
different approaches are used in conformally related frames, showing that the
torsion is not unique. The correspondingly modified Dirac equations in the
Einstein and String frames are shown to be separable. Furthermore, the massless
radial and angular wave-equations are examined, they show close similarity with
corresponding equations for the standard Kerr background. A generalization of
the Teukolsky equation for the pair-wise equal case is conjectured. We also
briefly analyze a technically sophisticated radial equation in the massive
case.
