  The non-local dependence of the fermion determinant on the gauge field limits
our ability of simulating Quantum Chromodynamics on the lattice. Here we
present a factorization of the gauge field dependence of the fermion
determinant based on an overlapping four-dimensional domain decomposition of
the lattice. The resulting action is block-local in the gauge and in the
auxiliary bosonic fields. Possible applications are multi-level integration,
master field simulations, and more efficient parallelizations of Monte Carlo
algorithms and codes.
