  Dynamical mean-field theory describes the impact of strong local correlation
effects in many-electron systems. While the single-particle spectral function
is directly obtained within the formalism, two-particle susceptibilities can
also be obtained by solving the Bethe-Salpeter equation. The solution requires
handling infinite matrices in Matsubara frequency space. This is commonly
treated using a finite frequency cut-off, resulting in slow linear convergence.
A decomposition of the two-particle response in local and non-local
contributions enables a reformulation of the Bethe-Salpeter equation inspired
by the dual boson formalism. The re-formulation has a drastically improved
cubic convergence with respect to the frequency cut-off, facilitating the
calculation of susceptibilities in multi-orbital systems considerably. This
improved convergence arises from the fact that local contributions can be
measured in the impurity solver. The dual Bethe-Salpeter equation uses the
fully reducible vertex which is free from vertex divergences. We benchmark the
approach on several systems including the spin susceptibility of strontium
ruthenate Sr$_2$RuO$_4$, a strongly correlated Hund's metal with three active
orbitals.
