Smolin, LeeShyam, Vasudev2020-07-272020-07-272020-07-272020-07-20http://hdl.handle.net/10012/16081Investigations relating the emergence of the radial direction in the holography, solvable irrelevant deformations of conformal eld theories and holographic entanglement entropy are reported. Emphasis is laid on how diffeomorphism invariance in the bulk emerges, in both the classical and quantum regimes. The computation of von Neumann entanglement and Renyi entropies in $T\bar{T}$ deformed conformal eld theories and their bulk dual quantities are presented. Further, the peculiar properties of the deformed theory that these quantities point to, are discussed. Finally, the connections between $T\bar{T}$ deformed partition functions and solutions to the radial Wheeler de Witt equation in three spacetime dimensions is presented.enTheoretical PhysicsQuantum GravityQuantum Field TheoryDoctoral Thesis