  Samarium hexaboride (SmB$_6$) is the first strongly correlated material with
a recognized non-trivial band-structure topology. Its electron correlations are
seen by inelastic neutron scattering as a coherent collective excitation at the
energy of 14 meV. Here we calculate the spectrum of this mode using a
perturbative slave boson method. Our starting point is the recently constructed
Anderson model that properly captures the band-structure topology of SmB$_6$.
Most self-consistent renormalization effects are captured by a few
phenomenological parameters whose values are fitted to match the calculated and
experimentally measured mode spectrum in the first Brillouin zone. A simple
band-structure of low-energy quasiparticles in SmB$_6$ is also modeled through
this fitting procedure, because the important renormalization effects due to
Coulomb interactions are hard to calculate by ab-initio methods. Despite
involving uncontrolled approximations, the slave boson calculation is capable
of producing a fairly good quantitative match of the energy spectrum, and a
qualitative match of the spectral weight throughout the first Brillouin zone.
We find that the "fitted" band-structure required for this match indeed puts
SmB$_6$ in the class of strong topological insulators. Our analysis thus
provides a detailed physical picture of how the SmB$_6$ band topology arises
from strong electron interactions, and paints the collective mode as
magnetically active exciton.
