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

TL;DR

This paper extends the $T\overline{T}$ deformation to higher-dimensional large-$N$ CFTs, establishing a holographic duality with semiclassical gravity in AdS with a finite cutoff and analyzing the deformation's effects on correlation functions.

Contribution

It generalizes the $T\overline{T}$ deformation to higher dimensions and derives the dual deformation in the bulk, including effects of background fields and matter theories.

Findings

Matching of deformed CFT correlators with bulk gravity calculations

Explicit construction of the dual deformation for matter theories

Demonstration of correlation function matching along the flow

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.