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kodama

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**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.

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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...

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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

LQG + Kodama respects the holographic principle via

**Ads/CFT correspondence**.