system in the continuum limit is along with renormalization the most interesting question
to be asking the Lightcone World Sheet.
2.2 Supersymmetric Gauge Theories
Casting pure Yang-Mills theory into Lightcone World Sheet form has been done by
Thorn [16] shortly after the appearance of the first article. Since a unified and slightly
refined representation for general Gauge theories later appeared [7] we skip over the
otherwise crucial step in the development of the Lightcone World Sheet constructions, and
turn right to Supersymmetric Gauge Theories.
2.2.1 SUSY Yang-Mills Quantum Field Theory
In their paper, Gudmundsson et. al. [7] build the extended =- 2 and = 4
super-symmetric Gauge theory by means of dimensional-reduction. This method starts off
with an = 1 super-symmetric Gauge theory in higher dimensions and then reduce the
theory to D = 4 by making the fields independent on the extra D 4 dimensions. This
automatically creates the correct number of fields for the extended super-symmetry. The
Gauge bosons associated with the extra dimensions become just the scalars when their
Gauge symmetry in the extra dimensions becomes a global symmetry and similarly the
higher dimensional representation of the Chfluid algebra generates just the right number
of fermions. This method is particularly useful on the Lightcone World Sheet because
making the fields independent upon the extra dimensions can easily be implemented by
setting the extra q components equal to zero on the boundaries of the sheet. They are still
allowed to fluctuate in the bulk, which allows them to participate in the crucial generation
of quartics from cubics as will be described in the next section. In order to carry out the
mapping of theories
(AN,D) -(1, 6) (N, D)= (2,4) and
(, D)= (1,10) (A, D)= (4,4)