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### Abstract

In recent years, there have been two independent but related developments in the study of irrelevant deformations in two dimensional quantum field theories (QFTs). The first development is the deformation of a two dimensional QFT by the determinant of the energy momentum stress tensor, commonly referred to as $T{\bar T}$ deformation. The second development is in two dimensional holographic field theories which are dual to string theory in asymptotically Anti-de Sitter (AdS) spacetimes. In this latter development, the deformation is commonly referred to as single-trace $T{\bar T}$ deformation. The single-trace $T{\bar T}$ deformation corresponds in the bulk to a string background that interpolates between AdS spacetime in the infrared (IR) and a linear dilaton spacetime (vacuum of little string theory (LST)) in the ultraviolet (UV). It serves as a useful tool and guide to better understand and explore holography in asymptotically AdS and non-AdS spacetimes in a controlled setting. In particular, it is useful to gain insights into holography in flat spacetimes. The dissertation is devoted to the study of single-trace $T{\bar T}$ deformation and its single-trace generalizations in theories with $U(1)$ currents, namely $J\bar T$ and $T\bar J$ deformations, in the context of gauge/gravity duality. In the dissertation I present new results in the study of holography in asymptotically non-AdS spacetimes. I discuss two point correlation functions in single-trace $T{\bar T}$ deformation, and entanglement entropy and entropic $c$-function in single-trace $T{\bar T}$, $J\bar T$ and $T\bar J$ deformations. I show that two point functions in position space have both real parts and imaginary parts. I also show that the imaginary parts are non-perturbative. The imaginary parts correspond in momentum space to branch cuts, which signal non-locality. I obtain exact result for entanglement entropy associated with a spatial region of finite size. I also show that in the UV for a particular combination of the deformation couplings the leading order dependence of the entanglement entropy on the size is given by a square root but not logarithmic function. Such power law dependence of the entanglement entropy on the size is quite distinct and interesting. I also give exact result for the entropic $c$-function and show that it is regularization schemes independent, positive and monotonic, which are similar to the behaviors observed in conventional local QFTs. I also discuss its distinctive features in the UV.