UCLA

The holographic duality, often coined the AdS/CFT correspondence, conjectures a relation between strongly coupled quantum systems and quantum gravity in higher-dimensional spacetimes. Gravitational theories in two and three dimensions are meaningful examples for classical and quantum exploration due to their unique characteristics, notably the absence of propagating bulk degrees of freedom and the presence of only boundary degrees of freedom, distinguishing them from higher-dimensional counterparts. These gravitational theories exhibit complex interactions when the bulk spacetime has a finite size, regulated by Zamolodchikov's double-trace irrelevant $T\overline{T}$ operator. This thesis aims to gain a holographic understanding of pure three-dimensional AdS$_3$ gravity and JT gravity under the influence of the $T\overline{T}$ deformation. Under a finite radial cutoff, these theories exhibit perturbative behavior that implies the emergence of the Nambu-Goto action for the corresponding boundary graviton action. We also conducted semi-classical calculations of observables related to finite-cutoff gravity and its dual $T\overline{T}$-deformed CFT description, including correlation functions involving stress tensors and gravitational Wilson lines, along with an analysis of their supersymmetric extensions. Additionally, we explored the implications of general stress tensor deformations within field-theoretic and holographic settings.