Abstract
We explore the program of the construction of the dual bulk theory in the flow equation approach. We compute the vacuum expectation value of the Einstein operator at the next to leading order in the 1/n expansion using a free O(n) vector model. We interpret the next to leading correction as the quantum correction to the cosmological constant of the AdS space. We finally comment on how to generalize this computation to matrix elements of the Einstein operator for excited states.
Highlights
It has passed two decades since the AdS/conformal field theory (CFT) correspondence was discovered [1]
In this situation this paper aims at proposing a new scheme to compute bulk dynamical observables from a boundary CFT by employing a new approach of the AdS/CFT incorporating a flow equation [29, 30, 31, 32], which was introduced to smear operators so as to resolve the UV divergence arising in the coincidence limit [33, 34, 35]
We have constructed the holographic space from the primary scalar field in a free massless O(n) vector model by a flow equation at the next to leading order (NLO) in the 1/n expansion
Summary
It has passed two decades since the AdS/CFT correspondence was discovered [1] (see [2, 3, 4] for reviews). In the holographic renormalization group approach by using the local renormalization group [21] (see [22, 23, 24, 25] and [26] for a review and references therein), it was shown in an abstract way that the bulk diffeomorphism invariance is fully encoded in the form of the Poisson algebra of the RG Hamiltonian by its Wess-Zumino consistency condition [27, 28] In this situation this paper aims at proposing a new scheme to compute bulk dynamical observables from a boundary CFT by employing a new approach of the AdS/CFT incorporating a flow equation [29, 30, 31, 32], which was introduced to smear operators so as to resolve the UV divergence arising in the coincidence limit [33, 34, 35]. In appendix B, we calculate various 2-point functions for the metric operator around its vacuum expectation value, which are necessary for the 1/n expansion
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