Large N analysis of T T ¯ $$ T\overline{T} $$ -deformation and unavoidable negative-norm states

Abstract

Abstract We study non-perturbative quantum aspects of T T ¯ $$ T\overline{T} $$ -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.

Keywords

• 2D Gravity
• Nonperturbative Effects
• Field Theories in Lower Dimensions
• Conformal Field Theory