| Summary: | Ph.D., Faculty of Science, University of Witwatersrand, 2011 === Operators in N = 4 super Yang-Mills theory with an R-charge of O(N2) are
dual to backgrounds which are asymtotically AdS5 S5. In this thesis we develop
e cient techniques that allow the computation of correlation functions
in these backgrounds. We nd that (i) contractions between elds in the
string words and elds in the operator creating the background are the eld
theory accounting of the new geometry, (ii) correlation functions of probes
in these backgrounds are given by the free eld theory contractions but with
rescaled propagators and (iii) in these backgrounds there are no open string
excitations with their special end point interactions; we have only closed
string excitations. Furthermore, these correlation functions are not well approximated
by the planar limit. The non-planar diagrams, which in the bulk
spacetime correspond to string loop corrections, are enhanced by huge combinatorial
factors. We show how these loop corrections can be resummed. As
a typical example of our results, in the half-BPS background of M maximal
giant gravitons we nd the usual 1=N expansion is replaced by a 1=(M +N)
expansion. Further, we nd that there is a simple exact relationship between
amplitudes computed in the trivial background and amplitudes computed in
the background of M maximal giant gravitons. We also nd strong evidence
for the BMN-type sectors suggested in arXiv:0801.4457. The problem of computing
the anomalous dimensions of (nearly) half-BPS operators with a large
R-charge is reduced to the problem of diagonalizing a Cuntz oscillator chain.
Due to the large dimension of the operators we consider, non-planar corrections
must be summed to correctly construct the Cuntz oscillator dynamics.
These non-planar corrections do not represent quantum corrections in the
dual gravitational theory, but rather, they account for the backreaction from
the heavy operator whose dimension we study. Non-planar corrections accounting
for quantum corrections seem to spoil integrability, in general. It is
interesting to ask if non-planar corrections that account for the backreaction
also spoil integrability. We nd a limit in which our Cuntz chain continues
to admit extra conserved charges suggesting that integrability might survive.
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