  The high-energy collective modes of particle-hole excitations across the
spin-orbit gap in $\rm Sr_2IrO_4$ are investigated using the transformed
Coulomb interaction terms in the pseudo-spin-orbital basis constituted by the
$J=1/2$ and $3/2$ states arising from spin-orbit coupling. With appropriate
interaction strengths and renormalized spin-orbit gap, these collective modes
yield two well-defined propagating spin-orbit exciton modes, with energy scale
and dispersion in excellent agreement with resonant inelastic X-ray scattering
(RIXS) measurements.
