Large N Analysis of $T\bar{T}$-deformation and Unavoidable Negative-norm States

Abstract

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.

arXiv comment1+20 pages, 1 figure

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Cited by in corpus (8)

• A pedagogical review on solvable irrelevant deformations of 2d quantum field theory
• Random Boundary Geometry and Gravity Dual of $T\bar{T}$ Deformation
• Infinite pseudo-conformal symmetries of classical $T\bar{T}$, $J\bar{T}$ and $J{T}_a$ - deformed CFTs
• $T\bar{T}$ Deformation of Stress-Tensor Correlators from Random Geometry
• $T\bar{T}$-deformation and Liouville gravity
• Perturbative renormalization of the $T\bar{T}$-deformed free massive Dirac fermion
• Nonperturbative aspects of two-dimensional $T\bar{T}$-deformed scalar theory from functional renormalization group
• Burgers Equation vs. Large $N$ Limit in $T\bar{T}$-deformed $O(N)$ Vector Model