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

TL;DR

This paper constructs a background-independent holographic dual for large central charge $Tar{T}$ deformed 2D conformal field theories by geometrizing the renormalization group flow into a three-dimensional Einstein-Hilbert action, ensuring covariance.

Contribution

It presents a novel background-independent holographic dual for $Tar{T}$ deformed CFTs by geometrizing their RG flow into an off-shell Einstein-Hilbert action, emphasizing covariance and background independence.

Findings

Constructed off-shell Einstein-Hilbert action from RG flow.

Ensured general covariance via Wess--Zumino conditions.

Achieved background independence in the holographic dual.

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.