$T\overline{T}$ Deformation: Introduction and Some Recent Advances
Song He, Yi Li, Hao Ouyang, Yuan Sun
TL;DR
This review surveys the $T\overline{T}$ deformation, a solvable yet irrelevant operator in two-dimensional QFT defined by $O_{T\overline{T}}$, and surveys its classical geometric realizations (random geometry, JT gravity, field-dependent coordinates) alongside quantum properties (non-locality, UV/IR mixing, exact spectra). It elucidates holographic connections via cutoff AdS and mixed boundary conditions, holographic entanglement entropy, and the JT gravity perspective, and then links these ideas to string theory through single-trace $T\overline{T}$ deformations, TsT transformations, and little string theory. The review also covers generalized TTbar-like deformations, nonrelativistic and higher-dimensional extensions, and discrete holography approaches, highlighting both the solvable structure and the nonlocal, boundary-graviton dynamics. Altogether, the work maps a cohesive landscape where TTbar-like flows illuminate emergent gravity, holography, and nonlocal QFT phenomena, while outlining promising future directions in UV completion, dualities, and beyond-large-$c$ analyses.
Abstract
This review explores recent advances in the theory of $T\bar{T}$ deformation, an irrelevant yet solvable deformation of quantum field theories defined via the quadratic form of the energy-momentum tensor. It addresses classical and quantum aspects, highlighting significant developments across various fields, including field theory, holography, and string theory. Classically, $T\bar{T}$ deformation manifests through multiple geometric interpretations, notably random geometry, Jackiw-Teitelboim-like gravity, and uniform light-cone gauge frameworks. For quantum aspects, the deformation introduces notable features such as non-locality, UV-IR mixing, solvable renormalization structures, and intriguing modifications to correlation functions and entanglement properties. Furthermore, the paper examines the profound relationship between $T\bar{T}$ deformation and holography, particularly within the mixed boundary conditions/cutoff AdS holography proposal and holographic entanglement entropy. Connections to string theory through single-trace deformations and their holographic duals further reveal the deformed structure of the worldsheet. This review synthesizes recent developments and outlines potential directions for future research in the study of $T\bar{T}$-like deformation.