Year: 2011
Type: dissertation
Abstract: In this thesis we introduce novel technology pertaining to the calculation of \ncertain classes of correlation functions in the half BPS, near BPS and multimatrix \nsectors (particularly the SU(2) sector) of N = 4 Super Yang-Mills \n(SYM) theory using the Schur polynomial and restricted Schur polynomial \nbases. This technology allows the detailed exploration of a host of physical \nquestions within the AdS/CFT correspondence. We rst treat multi-point \ncorrelators of restricted Schur polynomials which constitute a particularly \nconvenient basis for the SU(2) and general multi-matrix sectors of N = 4 \nSYM. We introduce a product rule for the restricted Schur polynomials, \nwhich, together with the two point correlator result of arXiv:0801.2061 allows \nus to compute exact multi-point correlators, in the free eld theory limit. \nThis facilitates the exploration of physical questions such as elucidating the \nappropriate degrees of freedom for a perturbative description of quantum \ngravity in the sectors under consideration. \nWe then treat the calculation of correlators of operators in the presence of \nlarge background operators with a R-charge of O(N2) that are dual to asymptotically \nAdS5 S5 backgrounds. Evaluating these correlators is a hard problem \nin general since the planar approximation fails. In this thesis we develop \ngeneral techniques, known as the \\cutting rules", that allow the computation \nof such correlators. Specializing to the LLM annulus geometry allows a \nnumber of concrete results to be derived. We then study the perturbation \ntheory of these correlators and identify new perturbative expansion parameters \nreplacing 1=N. Motivated by these results we explore new BMN-type \nsectors. \nFinally, we treat the problem of computing the anomalous dimensions of a \nclass of (nearly) half BPS operators with a large R-charge. This problem is \nreduced to the problem of diagonalizing a Cuntz oscillator chain. Non-planar \ncorrections must be summed to correctly construct the Cuntz oscillator dynamics. \nWe explore whether these non-planar corrections that account for \nbackreaction from the heavy operator rather than quantum corrections in the \ndual gravitational theory also spoil integrability as is generally the case with \nquantum corrections. We nd a limit in which our Cuntz chain continues to \nadmit extra conserved charges suggesting that integrability might survive.
Author: Michael Stephanou
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2171860779