  A recent proposal relates two dimensional holographic conformal field
theories deformed by the integrable $T\bar{T}$ flow to AdS$_3$ with a finite
radial cutoff. We investigate this proposal by studying perturbative
correlation functions on the two sides. For low point correlators of the stress
tensor, we successfully match the deformed CFT results at large central charge
to bulk results obtained in classical pure gravity. The deformed CFT also
provides definite predictions for loop corrections in the bulk. We then include
matter fields in the bulk. To reproduce the classical bulk two-point function
of a scalar operator we show that the deformed CFT needs to be augmented with
double trace scalar operators, with the $T\bar{T}$ operator yielding
corrections corresponding to loops in the bulk.
