CHAPTER 1
INTRODUCTION
In this dissertation we will present a connection between field theories and string
theory which has enjoyed an increasing interest by researchers in the field of theoretical
high energy physics. This is true especially since Maldacena proposed that IIB supersting
theory on an AdS5 x S5 background is equivalent to supersymmetric Yang-Mills field theory
with extended A = 4 supersymmetry (a (.. iii t i'e called the AdS/CFT correspondence
[1]). This is the view that although string theory has so far been unsuccessful in its task of
predicting experimental results as an all inclusive th., .ii v-of- i. iii,.:- in its own right, its
techniques are potentially applicable in describing mathematically limits or views of older
field theories which themselves have a strong experimental foundation.
The string techniques in field theory have a myriad of possible applications. Wherever
the standard perturbative advances fail, some other technique is needed, the confinement
problem in QCD being an obvious example. Mechanisms which have been proposed
to confine the quarks of QCD include color flux tubes and gluon chains. A complete
description of the mechanism would of course eventually involve a stringy limit of
the underlying field theory. It may be that a string description of particular physical
mechanisms, and not of the theory as a whole, is what will prevail. The idea dates back
to 1970 [2] and [3] and was further established by t'Hooft in 1974 [4]. t'Hooft's approach
was to construct a systematic expansion in 1/NA for a general field theory, where the
meaning of N, could be made definite for "non-Gauge" theories by means of a global
SU(Nc) symmetry group acting on a matrix of fields. The 1/NA expansion turned out to
single out planar Feynman diagrams in expressions for observables of the theory, planar
in the sense that in his double-line notation .r v could be drawn on a plane i.e., with no
lines intersecting. When the planar diagrams in t'Hooft's original work were selected, the