Large N analysis of $$ T\overline{T} $$-deformation and unavoidable negative-norm states
Junichi Haruna, Takaaki Ishii, H. Kawai, K. Sakai, Kentaroh Yoshida
Abstract
A bstract We study non-perturbative quantum aspects of $$ T\overline{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> -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.