Background independent holographic dual to $T\bar{T}$ deformed CFT with large central charge in 2 dimensions

Abstract

The geometerization of the renormalization group flow triggered by the $T\bar{T}$ deformation of large $c$ conformal field theories in two dimensions is presented. This entails the construction of the off shell Einstein-Hilbert action in three dimensions from said renormalization group flow. The crucial ingredient to this construction will be the encoding of general covariance in the emergent bulk theory in a very particular form of the Wess--Zumino consistency conditions. The utilisation of the local renormalization group, which requires putting the theory under consideration on an arbitrary background geometry, supplemented by the aforementioned covariance condition ensures that the whole construction is background independent.