  The numerical computations of many quantities of theoretical and
phenomenological interest are plagued by statistical errors which increase
exponentially with the distance of the sources in the relevant correlators.
Notable examples are baryon masses and matrix elements, the hadronic vacuum
polarization and the light-by-light scattering contributions to the muon g-2,
and the form factors of semileptonic B decays. Reliable and precise
determinations of these quantities are very difficult if not impractical with
state-of-the-art standard Monte Carlo integration schemes. I will review a
recent proposal for factorizing the fermion determinant in lattice QCD that
leads to a local action in the gauge field and in the auxiliary boson fields.
Once combined with the corresponding factorization of the quark propagator, it
paves the way for multi-level Monte Carlo integration in the presence of
fermions opening new perspectives in lattice QCD. Exploratory results on the
impact on the above mentioned observables will be presented.
