  We study non-perturbative quantum aspects of $T\bar{T}$-deformation of a free
$O(N)$ vector model by employing the large $N$ limit. It is shown that bound
states of the original field appear and inevitably become negative-norm states.
In particular, the bound states can be regarded as the states of the conformal
mode in a gravitational theory, where the Liouville action is induced with the
coefficient proportional to the minus of central charge. To make the theory
positive-definite, some modification is required so as to preserve
diffeomorphism invariance due to the Faddeev-Popov ghosts with a negative
central charge.
