  Four dimensional BF theory admits a natural coupling to extended sources
supported on two dimensional surfaces or string world-sheets. Solutions of the
theory are in one to one correspondence with solutions of Einstein equations
with distributional matter (cosmic strings). We study new (topological field)
theories that can be constructed by adding extra degrees of freedom to the two
dimensional world-sheet. We show how two dimensional Yang-Mills degrees of
freedom can be added on the world-sheet, producing in this way, an interactive
(topological) theory of Yang-Mills fields with BF fields in four dimensions. We
also show how a world-sheet tetrad can be naturally added. As in the previous
case the set of solutions of these theories are contained in the set of
solutions of Einstein's equations if one allows distributional matter supported
on two dimensional surfaces. These theories are argued to be exactly
quantizable. In the context of quantum gravity, one important motivation to
study these models is to explore the possibility of constructing a background
independent quantum field theory where local degrees of freedom at low energies
arise from global topological (world-sheet) degrees of freedom at the
fundamental level.
