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

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