THE LARGE N EXPANSION
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lies in the inadequacy of our understanding of string theory. This will be
discussed in Chapter 10. Another problem is related to the following
clumsy feature of equation (8.93). This equation is true only for a
definite regularization of gauge theory and of string theory. Therefore it
is possible that the “correct” string theory will not satisfy (8.93) just
because it has been regularized in a different way. It makes attempts to
solve (8.93) by the use of the string ansatz very difficult. Perhaps it will
be easier to compare directly the small distance behaviour in the string
theory with the one described by asymptotically free gluons. The
situation with the loop equations, described above, is reminiscent of the
one with Shrodinger equations for field theory. Although these functional equations are in principle correct for the regularized theory, and
can be renormalized with some effort, their practical use up to now has
been quite limited. Instead, it appears more convenient to study directly
their solutions in the form of functional integrals.
In the next chapter we shall describe a similar approach to the theory
of strings.