  We propose an efficient dual boson scheme, which extends the DMFT paradigm to
collective excitations in correlated systems. The theory is fully
self-consistent both on the one- and on the two-particle level, thus describing
the formation of collective modes as well as the renormalization of electronic
and bosonic spectra on equal footing. The method employs an effective impurity
model comprising both fermionic and bosonic hybridization functions. Only
single- and two-electron Green's functions of the reference problem enter the
theory, due to the optimal choice of the self-consistency condition for the
effective bosonic bath. We show that the theory is naturally described by a
dual Luttinger-Ward functional and obeys the relevant conservation laws.
