  Pure gauge lattice QCD at arbitrary D is considered. Exact integration over
link variables in an arbitrary D-volume leads naturally to an appearance of a
set of surfaces filling the volume and gives an exact expression for functional
of their boundaries. The interaction between each two surfaces is proportional
to their common area and is realized by a non-local matrix differential
operator acting on their boundaries. The surface self-interaction is given by
the QCD$_2$ functional of boundary. Partition functions and observables (Wilson
loop averages) are written as an averages over all configurations of an
integer-valued field living on a surfaces.
