in perturbation theory according to the topology of a sheet which immediately calls for
an analogy with a string theory world sheet. Lightcone variables offer a parametrization
of the sheet on which one would draw Feynman diagrams, using x+ and p+ and further
promoting x+ to an evolution parameter. Each Feynman diagram can in such a way be
seen as a world sheet as shown in Figure 1-2.
The above way of identifying each Feynman diagram with a world sheet was further
implemented by Bardakci and Thorn and is the basis for the Lightcone World Sheet
formalism, which is the framework on which the work in this thesis is based. As was
discussed above, the string-field theory connection has been an active subject of research
ever since the Maldacena AdS/CFT correspondence emerged. The development of the
Lightcone World Sheet idea is an rare example of the theoretical attempt at constructing
a string world sheet which sums planar diagrams of field theory. More emphasis has
been put into the opposite view, i.e., to recover field theoretic physics from the string
formulation. As was pointed out in Thorn and Tran [8] the next task is to develop a
tractable framework for extracting the physics from this new world-sheet formalism. The
first steps of organizing the renormalization in this picture were taken alongside developing
the supersymmetric Lightcone World Sheet [7] and are further repeated here as part of the
graduate work of the author. The necessary conclusion was later published in an article
which summarized the renormalized f3 world-sheet [9].
Previous work on summing planar diagrams should not be forgotten. Ideas and
methods of considering special cases of planar diagrams, those which would describe
simple models for forces between quarks, have been pursued. Among those, fishnet
diagrams are particularly interesting [10] because of how 'l. v, or at least fishnet-like
diagrams, seem to be emerging from the Monte Carlo studies presented later in this
dissertation.
The conclusion is that fishnets come about as particular sub-sums in the sum over
all planar diagrams if viewed in the Lightcone World Sheet picture; in other words, ],l v