  We present intermediate results of an ongoing investigation which attempts a
generalization of the well known one-loop Bern Kosower rules of Yang-Mills
theory to higher loop orders. We set up a general procedure to extract the
field theoretical limit of bosonic open string diagrams, based on the sewing
construction of higher loop world sheets. It is tested with one- and two-loop
scalar field theory, as well as one-loop and two-loop vacuum Yang-Mills
diagrams, reproducing earlier results. It is then applied to two-loop two-point
Yang-Mills diagrams in order to extract universal renormalization coefficients
that can be compared to field theory. While developing numerous technical tools
to compute the relevant contributions, we hit upon important conceptual
questions: Do string diagrams reproduce Yang-Mills Feynman diagrams in a
certain preferred gauge? Do they employ a certain preferred renormalization
scheme? Are four gluon vertices related to three gluon vertices? Unfortunately,
our investigations remained inconclusive up to now.
