by the same means of qualitative hand-waving as up until now) how the complete set of
vertices are generated by local insertions on the world sheet.
2.2.2 SUSY Yang-Mills as a Lightcone World Sheet
The construction of the world sheet local action is analogous to the scalar matrix field
case. The path integral reproduces first the mixed representation propagator and then
adds interaction vertices by means of the spin system si as before. Recall that the q-s
now have D 2 components with all but two identically zero on all boundaries. Clearly,
if the rich particle structure of other field theories is to fit into the picture, then all field
theoretic propagators must (and do) have the same simple exponential form as the scalar
propagator, times, at most, Kronecker deltas that describe the flow of spin and other
internal quantum numbers. T]. r, Fore the expression (2-6) is universal for the Lightcone
World Sheet form of a field theory. The general construction of the SUSY Lightcone World
Sheet follows very much the same procedure as the scalar case with a few fundamental
differences. In the Lightcone World Sheet picture the fundamental propagation is that of
momentum, represented by the width of the strip. Such things as the field theories' rich
collection of particles must be propagated through the sheet by means of "flavoring" the
strip (lattice sites) with dynamical variables. Furthermore, the vertices must come out of
local alterations on the world sheet, if the picture is to retain its elegance and its relation
to string theory. Instead of repeating the systematic construction of the world sheet theory
from the original work [7, 16], and as was done for the scalar theory above, we comment
on the main issues briefly. The discussion here is in the form of an existence argument,
we show how a Lightcone World Sheet description of super-symmetric Yang-Mills theory
could be constructed. The interested reader is referred to the original work for a more
thorough and full picture.
After seeing the construction of the Lightcone World Sheet for the scalar matrix
theory, the first questions one needs to address when turning to SUSY Yang-Mills are the
following: