Holographic computation of quantum correction in the bulk - Dual - - PowerPoint PPT Presentation
Holographic computation of quantum correction in the bulk - Dual covariant perturbation - 29 May 2019 @ YITP Quantum Information and String Theory 2019 Shuichi Yokoyama Yukawa Institute for Theoretical Physics PTEP 2019 (2019) no.4, 043
S.Aoki-J.Balog-SY PTEP 2019 (2019) no.4, 043
Ref.
Quantum Information and String Theory 2019
Consider Einstein-Hilbert action in any dimensions R: Ricci scalar, GN 〜 κ2: Newton constant
Consider Einstein-Hilbert action in any dimensions Perturbation is the same as a usual gauge theory, say Yang-Mills theory: R: Ricci scalar, GN 〜 κ2: Newton constant
Consider Einstein-Hilbert action in any dimensions Renormalizability in QFT depends on the dimension of the coupling constant (CC): Perturbation is the same as a usual gauge theory, say Yang-Mills theory: Dimension of the Newton constant: R: Ricci scalar, GN 〜 κ2: Newton constant
Consider Einstein-Hilbert action in any dimensions Renormalizability in QFT depends on the dimension of the coupling constant (CC): Perturbation is the same as a usual gauge theory, say Yang-Mills theory: Dimension of the Newton constant: If D > 2, the κ has the negative mass dimension. → Non-renormalizable. R: Ricci scalar, GN 〜 κ2: Newton constant
Consider Einstein-Hilbert action in any dimensions R: Ricci scalar, κ2: Newton constant Perturbation is the same as a usual gauge theory, say Yang-Mills theory:
Renormalizability in QFT depends on the dimension of the coupling constant (CC): Dimension of the Newton constant: If D > 2, the κ has the negative mass dimension. → Non-renormalizable.
Consider Einstein-Hilbert action in any dimensions R: Ricci scalar, κ2: Newton constant Perturbation is the same as a usual gauge theory, say Yang-Mills theory:
Renormalizability in QFT depends on the dimension of the coupling constant (CC):
Dimension of the Newton constant: If D > 2, the κ has the negative mass dimension. → Non-renormalizable.
[‘t Hooft ’93, Susskind ‘94]
[Denes Gabor '47]
[Maldacena ’97] [‘t Hooft ’93, Susskind ‘94]
[Denes Gabor '47]
[Maldacena ’97] [‘t Hooft ’93, Susskind ‘94]
[Kachru-Liu-Mulligan ‘08] [Denes Gabor '47] [Son ’08, Balasubramanian-McGreevy ‘08]
[Maldacena ’97] [‘t Hooft ’93, Susskind ‘94]
[Son ’08, Balasubramanian-McGreevy ‘08] [Kachru-Liu-Mulligan ‘08] [Denes Gabor '47]
Consider a free O(n) vector model and smear a vector field va(x) by a free flow equation:
flowed operator Consider a free O(n) vector model and smear a vector field va(x) by a free flow equation:
flowed operator
[Albanese et al. (APE) '87] [Narayanan-Neuberger '06]
Claim: UV singularity in the coincidence limit is resolved. Consider a free O(n) vector model and smear a vector field va(x) by a free flow equation:
flowed operator
[Albanese et al. (APE) '87] [Narayanan-Neuberger '06]
Claim: UV singularity in the coincidence limit is resolved. Consider a free O(n) vector model and smear a vector field va(x) by a free flow equation:
NOTE:
(Dimensionless normalized operator)
“Operator renormalization” [Aoki-Kikuchi-Onogi ’15] [Aoki-Balog-Onogi-Weisz ’16,'17]
NOTE:
(Dimensionless normalized operator)
(Metric operator and induced metric)
“Operator renormalization” [Aoki-Kikuchi-Onogi ’15] [Aoki-Balog-Onogi-Weisz ’16,'17]
[Aoki-Kikuchi-Onogi ’15] [Aoki-Balog-Onogi-Weisz ’16,'17] NOTE:
(Dimensionless normalized operator)
(Metric operator and induced metric)
“Operator renormalization” [Aoki-SY '17]
Comment: An induced metric defined in this way matches the information metric.
NOTE:
(Dimensionless normalized operator)
(Metric operator and induced metric)
“Operator renormalization” [Aoki-SY '17] In the current case,
Comment: An induced metric defined in this way matches the information metric.
[Aoki-Kikuchi-Onogi ’15] [Aoki-Balog-Onogi-Weisz ’16,'17]
➡ !
Hermitian conjugate!!
[Aoki-SY '17]
Hermitian conjugate!!
CLAIM: This induced Einstein tensor is expected to describe that of dual quantum gravity.
CLAIM: This induced Einstein tensor is expected to describe that of dual quantum gravity. In particular, let us compute LHS in the 1/n expansion: Leading Order (LO) Next to Leading Order (NLO) Classical geometry Quantum correction
CLAIM: This induced Einstein tensor is expected to describe that of dual quantum gravity. In particular, let us compute LHS in the 1/n expansion: Leading Order (LO) Next to Leading Order (NLO) Classical geometry Quantum correction NOTE: This framework itself should be applicable to other formulation!
Perturbation of pregeometric operators:
Perturbation of pregeometric operators:
Consider free O(n) vector model.
①! Consider the vacuum state. The stress tensor is only cosmological constant. ➡ !
Consider free O(n) vector model. ②! Expand the pregeometric operators around the vacuum. (Dual covariant perturbation)
①! Consider the vacuum state. The stress tensor is only cosmological constant. ➡ !
Consider free O(n) vector model. ②! Expand the pregeometric operators around the vacuum. (Dual covariant perturbation) ③! Taking the VEV:
①! Consider the vacuum state. The stress tensor is only cosmological constant. ➡ !
Consider free O(n) vector model. ②! Expand the pregeometric operators around the vacuum. (Dual covariant perturbation) ③! Taking the VEV:
①! Consider the vacuum state. The stress tensor is only cosmological constant. ➡ !
Consider free O(n) vector model. ②! Expand the pregeometric operators around the vacuum. (Dual covariant perturbation) ③! Taking the VEV:
①! Consider the vacuum state. The stress tensor is only cosmological constant. ➡ ! Remark 1: The induced metric does not receive the quantum correction. Remark 2: The dual gravity theory is renormalizable in this framework.
working in progress [Aoki-Balog-SY]
working in progress [Aoki-Balog-SY]