Holography at finite cutoff with a $T^2$ deformation

TL;DR

This work generalizes the $T\overline{T}$ deformation to higher-dimensional, large-$N$ CFTs by defining a boundary EFT that flows with a finite radial cutoff $r_c$ in AdS. The authors derive the deformation via two gravity-inspired methods (trace/Brown-York and Wheeler-DeWitt), extend it to include matter couplings, and map bulk quantities to boundary data through a precise $\lambda\leftrightarrow r_c$ dictionary. They demonstrate striking agreement between boundary EFT observables (energy spectrum, thermodynamics, and two-point functions) and bulk quantities at finite cutoff, including scalar, current, and stress-tensor sectors, and provide a random-metric interpretation via Hubbard-Stratonovich. The results establish a coherent holographic dictionary at finite cutoff with clear implications for UV completion, causality, and potential connections to higher-dimensional generalizations of holography.

Abstract

We generalize the $T\overline{T}$ deformation of CFT$_2$ to higher-dimensional large-$N$ CFTs, and show that in holographic theories, the resulting effective field theory matches semiclassical gravity in AdS with a finite radial cutoff. We also derive the deformation dual to arbitrary bulk matter theories. Generally, the deformations involve background fields as well as CFT operators. By keeping track of these background fields along the flow, we demonstrate how to match correlation functions on the two sides in some simple examples, as well as other observables.