Abstract
We study non-perturbative quantum aspects of Toverline{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.
Highlights
JHEP04(2020)127 the T T-deformation at the classical level
We study non-perturbative quantum aspects of T T-deformation of a free O(N ) vector model by employing the large N limit
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
Summary
We will consider an infinitesimal T T-deformation of a free O(N ) vector model. Note here that 0|Cμν|0 = 0 because Cμν is traceless and the vacuum is invariant under the translations and the Lorentz transformations This value satisfies the condition of the stationary action. We regulate the first term on the left-hand side of eq (2.10) by Pauli-Villars (PV) regulators It turns out two regulators are necessary because quadratic and logarithmic divergences appear in the following calculation. By adopting the PV regularization, the regularized trace term in (2.10) is evaluated as 1 ∂2 + (1 + C )m20 − iε i → This equation contains the quadratic and logarithmic divergent parts as M1 → ∞. These are controlled by renormalizing Λ0, not α0!2 This is the reason why the Λ0C term was added to the action (2.4) in (2.6) in advance
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