Does Ads/CFT correspondence apply to LQG Kodama state?

In summary, the paper discusses the unique properties of the Kodama state in loop quantum gravity, which is an exact solution to the constraints of canonical quantum gravity and has a semiclassical limit of (anti)de Sitter space. However, the state is faced with several challenges, including non-normalizability, CPT violation, negative energies, non-invariance under large gauge transformations, and reality constraints. The authors suggest that these problems may be addressed by the AdS/CFT correspondence, as AdS is dual to CFT in one less dimension.
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kodama
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first paperhttp://arxiv.org/abs/hep-th/0209079
Quantum gravity with a positive cosmological constant
Lee Smolin
59 pages

"A quantum theory of gravity is described in the case of a positive cosmological constant in 3+1 dimensions. Both old and new results are described, which support the case that loop quantum gravity provides a satisfactory quantum theory of gravity. These include the existence of a ground state, discoverd by Kodama, which both is an exact solution to the constraints of quantum gravity and has a semiclassical limit which is deSitter spacetime. The long wavelength excitations of this state are studied and are shown to reproduce both gravitons and, when matter is included, quantum field theory on deSitter spacetime. Furthermore, one may derive directly from the Wheeler-deWitt equation, Planck scale, computable corrections to the energy-momentum relations for matter fields. This may lead in the next few years to experimental tests of the theory.
To study the excitations of the Kodama state exactly requires the use of the spin network representation, which is quantum deformed due to the cosmological constant. The theory may be developed within a single horizon, and the boundary states described exactly in terms of a boundary Chern-Simons theory. The Bekenstein bound is recovered and the N bound of Banks is given a background independent explanation.
The paper is written as an introduction to loop quantum gravity, requiring no prior knowledge of the subject. The deep relationship between quantum gravity and topological field theory is stressed throughout. "

second paper

http://arxiv.org/abs/gr-qc/0611073
Generalizing the Kodama State I: Construction
Andrew Randono
First part in two part series, 20 pages

The Kodama State is unique in being an exact solution to all the ordinary constraints of canonical quantum gravity that also has a well defined semi-classical interpretation as a quantum version of a classical spacetime, namely (anti)de Sitter space. However, the state is riddled with difficulties which can be tracked down to the complexification of the phase space necessary in its construction.
^
from the paper

In this respect the Kodama state is unique. Not only is the state an
exact solution to all the constraints of canonical quantum gravity, a rarity in itself, but it also has a well defined physical interpretation as the quantum analogue of a familiar classical spacetime, namely de Sitter or anti-de Sitter space depending on the sign of the cosmological constant[1, 2, 3]. Thus, the state is a candidate for the fulfillment of one of the distinctive advantages of a non-perturbative approach over perturbative techniques: the former has the potential to predict the purely quantum mechanical ground state on which perturbation theory can be based. In addition, the Kodama state has many beautiful mathematical properties relating the seemingly disparate fields of abstract knot theory and quantum field theory on a space of connections[4].

In particular, the exact form of the state is known in both the connection representation where it is the exponent of the Chern-Simons action, and in the q-deformed spin network representation where it is a superposition of 2...

^

Since Kodama state semiclassical limit is (anti)de Sitter space, LQG + Kodama state gives you Ads/CFT correspondence.

LQG + Kodama respects the holographic principle via Ads/CFT correspondence.
 
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I think I said this in some other thread, but I'm not sure the OP has seen it: http://arxiv.org/abs/0905.3627. The authors are studing LQG, but they mysteriously find an AdS/CFT formula popping up.
 
  • #3
atyy said:
I think I said this in some other thread, but I'm not sure the OP has seen it: http://arxiv.org/abs/0905.3627. The authors are studing LQG, but they mysteriously find an AdS/CFT formula popping up.

ive not seen that paper.

the above researchers claim that LQG+Kodama gives (anti)DS.

==quote Randono paper A page 3==

1.1 Problems
Despite all of these positive attributes of the Kodama state, the state is
plagued with problems. Among these are the following:

Non-normalizability: The Kodama state is not normalizable under
the kinematical inner product, where one simply integrates |Ψ|2 over all values of the complex Ashtekar connection. The state is not known to be normalizable under a physical inner product defined by, for example, path integral methods. Linearized perturbations around the state are known to be non-normalizable under a linearized inner product[7].

CPT Violation: The states are not invariant under CPT[8]. This is particularly poignant objection in view of the CPT theorem of perturbative quantum field theory, which connects CPT violation with Lorentz violation. It is not known if the result carries over to non-perturbative quantum field theory, but it has yet to be demonstrated that the Kodama state does not predict Lorentz violation.

Negative Energies: It has been argued by analogy with a similar non-perturbative Chern-Simons state of Yang-Mills theory that the Kodama state necessarily contains negative energy sectors[8]. If the energy of one sector of the state is strictly positive, the CPT inverted state will necessarily contain negative energy sectors.

Non-Invariance Under Large Gauge Transformations: Although the state is invariant under the small gauge transformations generated by the quantum constraints, it is not invariant under large gauge transformations where it changes by a factor related to the winding number of the map from the manifold to the gauge group. However, it has been argued that the non-invariance of the Kodama state under large gauge transformations give rise to the thermal properties of de Sitter spacetime2[9]. Thus, non-invariance under large gauge transformations could be a problem or a benefit, but it is deserving of mention.

Reality Constraints: The Lorentzian Kodama state is a solution to the quantum constraints in the Ashtekar formalism where the connection is complex. To obtain classical general relativity one must implement reality conditions which ensure that the metric is real. It is an open problem as to how to implement these constraints on a general state. Generally it is believed that the physical inner product will implement the reality constraints, but this could change the interpretation of the state considerably.
^

LQG+ Kodama gives AdS but has those problems.

since AdS is dual to CFT in one less dimension, does CFT address those problems? just map those problems into the corresponding CFT
 

Related to Does Ads/CFT correspondence apply to LQG Kodama state?

1. What is Ads/CFT correspondence?

Ads/CFT correspondence is a theoretical framework in physics that relates two seemingly different theories, Anti-de Sitter space (Ads) and conformal field theory (CFT). It suggests that these two theories are actually dual to each other, meaning that they can be described by the same mathematical equations but in different dimensions. This correspondence has been extensively studied in the context of string theory and has led to new insights into the nature of gravity and quantum field theory.

2. What is LQG Kodama state?

LQG Kodama state is a specific state in Loop Quantum Gravity (LQG) theory. LQG is a proposed quantum theory of gravity that attempts to reconcile general relativity and quantum mechanics. The Kodama state is a coherent state that was introduced by Hideo Kodama in 1990 and is used to quantize the gravitational field in LQG. It has been studied as a potential candidate for the quantum state of the early universe.

3. Does Ads/CFT correspondence apply to LQG Kodama state?

There is ongoing debate and research on whether Ads/CFT correspondence can be applied to LQG Kodama state. Some studies suggest that there may be a connection between the two theories, while others argue that the two are fundamentally different and cannot be reconciled. Further research and exploration are needed to fully understand the potential relationship between Ads/CFT and LQG Kodama state.

4. What implications would the application of Ads/CFT correspondence to LQG Kodama state have?

If it is found that Ads/CFT correspondence does indeed apply to LQG Kodama state, it could have significant implications for our understanding of quantum gravity and the early universe. It could potentially provide a more complete and unified theory of gravity and help us better understand the nature of space and time.

5. What other areas of physics could be impacted by the application of Ads/CFT correspondence to LQG Kodama state?

The application of Ads/CFT correspondence to LQG Kodama state could have far-reaching effects, not only in the field of quantum gravity but also in other areas of physics. It could potentially shed light on the behavior of matter at the quantum level, the nature of black holes, and the properties of spacetime. It could also have implications for astrophysics and cosmology, providing a deeper understanding of the universe on both a microscopic and macroscopic scale.

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