where a8 = g2/27.
3.2.2 Simplification: The World Sheet Picture
It is however more interesting to do the calculation above in a slightly different
manner. It is --'-'. -1. .1 by the world sheet picture, that one combine self energy and
vertex diagrams at each value of the discrete p+ of the loop. If we back up the above
calculation and consider the contribution to charge renormalization before the p+ sum is
done we have
(g3 n(/) K^M1 2 1 1 2 fg(1/11.)
(1gluOns)AAV 42 ln(1/a)3_Y(A { K + .- + _1- + } .
-(1 2), (3-47)
The first three logarithmically divergent terms in the I summands again represent the
entanglement of infrared and ultraviolet divergences. These terms will cancel against terms
from the self-energy, so that the entangled divergences never arise. We shall see this better
in the next section, when the full particle content is taken into account.
3.3 Adding SUSY Particle Content: Fermions and Scalars
The proper one loop correction to the cubic vertex is represented by a Feynman
triangle graph appearing in the world sheet as shown in Fig. 3-2.
With the external particles of Fig. 3-2 restricted to be gluons (vector bosons) the one
loop renormalization of the gauge coupling requires calculating the triangle graph for the
different particles of the theory running around the loop. In the following subsections it
will be useful to employ the "complex x^ = x1 + ix2 and xv = x1 ix2 for the first
two components of any transverse vector x.
Fermions