Carlson, Warren Anthony2024-11-192024-11-192023-07Carlson, Warren Anthony. (2023). The Large N Limit of Heavy Operator Excitations. [PhD thesis, University of the Witwatersrand, Johannesburg]. https://hdl.handle.net/10539/42758https://hdl.handle.net/10539/42758Thesis presented in fulfillment of the requirements for the degree of Doctor of Philosophy, to the Faculty of Science, School of Physics, University of the Witwatersrand, Johannesburg, 2023.Operators with bare dimension of order N are studied. These are restricted Schur polynomials labeled by Young diagrams with two long rows or two long columns and are heavy operators in the large N limit. A dramatic simplification of the action of the dilatation operator on these states is found, where the diagonalization of the dilatation operator reduces to solving three-term recursion relations. The solutions to these recursion relations reduce the spectrum of the dilatation operator to that of decoupled harmonic oscillators, showing that these systems are integrable at large N. Then, generating functions for bound states of two giant gravitons are constructed and an extension to more than two giant gravitons is sketched. These generating functions are integrals over auxiliary variables that encode the symmetrization and anti-symmetrization of the fields in the restricted Schur polynomials and give a simple construction of eigenfunctions of the dilatation operator. These generating functions are shown to be eigenfunctions of the dilatation operator in the large N limit. As a byproduct, this construction gives a natural starting point for systematic 1/N expansions of these operators. This includes the prospect to generate asymptotic representations of the symmetric group and its characters via the restricted Schur polynomials. Finally, the asymptotic expansion of the three-point function is computed in three BMN limits by varying one parameter in the large N limit. It is argued that these asymptotic expansions encode non-perturbative effects and are related by a parametric Stokes phenomenon.en©2023 University of the Witwatersrand, Johannesburg. All rights reserved. The copyright in this work vests in the University of the Witwatersrand, Johannesburg. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of University of the Witwatersrand, Johannesburg.AdS/CFT CorrespondenceGauge-Gravity CorrespondenceUCTDSDG-4: Quality educationThesisUniversity of the Witwatersrand, Johannesburg