Large N analysis of T(T)over-bar-deformation and unavoidable negative-norm states

We study non-perturbative quantum aspects of TT over bar -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.