Murali, Harish2026-06-242026-06-242026-06-242026-06-19https://hdl.handle.net/10012/23670This thesis explores quantum gravity by studying large-N gauge theories and matrix models. In particular, it focuses on operators whose charges scale as N^2, which we dub huge operators, so that they are heavy enough to backreact on the dual bulk geometry. In the first part, we study protected sectors of N = 4 super Yang-Mills theory, where supersymmetry gives enough control to ask finite-N questions beyond the planar limit. We analyze huge 1/2-BPS operators and show that their exact combinatorics reorganizes, at large N, into matrix models and integrable HCIZ fluid flows. We also study the 1/16-BPS sector relevant for supersymmetric black holes, emphasizing the role of finite-N trace relations and analytic continuation in the number of colors. In the second part, we turn to simpler matrix models as laboratories for holographic ideas such as universality, and commutativity. We show that huge deformations can produce universal eigenvalue densities in strong-coupling regimes, and we clarify the role of fermions in ensuring commutativity at strong coupling. Together, these results give concrete boundary descriptions of backreacted geometries, finite-N effects, and strong coupling dynamics.enBPS correlatorsmatrix modelsholographyDoctoral Thesis