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• W2146078763 abstract "Operators in N = 4 super Yang-Mills theory with an R-charge of O(N) are dual to backgrounds which are asymtotically AdS5×S. In this thesis we develop efficient techniques that allow the computation of correlation functions in these backgrounds. We find that (i) contractions between fields in the string words and fields in the operator creating the background are the field theory accounting of the new geometry, (ii) correlation functions of probes in these backgrounds are given by the free field 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 find the usual 1/N expansion is replaced by a 1/(M +N) expansion. Further, we find 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 find 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 find a limit in which our Cuntz chain continues to admit extra conserved charges suggesting that integrability might survive." @default.
• W2146078763 created "2016-06-24" @default.
• W2146078763 creator A5066871167 @default.
• W2146078763 date "2011-09-16" @default.
• W2146078763 modified "2023-09-27" @default.
• W2146078763 title "Large R-charge operators in N =4 super Yang-Mills and their gravity duals" @default.
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