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arivero

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arivero

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- #27

marcus

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here is a sample exerpt from the Madrid talk, slides 14 - 16:

==quote==

First of all, I am only going to consider the case of negative cosmological constant.

Currently there is some suspicion that quantum gravity with Lambda > 0 doesn't exist non-perturbatively (in any dimension) with positive cosmological constant. The reason for this is that it does not appear to be possible, with Lambda > 0, to define precise observables. This is natural if it is the case that a world with positive cosmological constant (like the one we may be living in) is always unstable.

If that is so, then a world with Lambda > 0 doesn't really make sense as an exact theory in its own right but (like an unstable particle) must be studied as part of a larger system.

Whether that is the right interpretation or not, since I don't know how to define any precise observables, I don't know what it would mean to try to solve 2+1-dimensional gravity with Lambda > 0, since it isn't clear what we'd want to compute.

==endquote==

Any comment?

==quote==

First of all, I am only going to consider the case of negative cosmological constant.

Currently there is some suspicion that quantum gravity with Lambda > 0 doesn't exist non-perturbatively (in any dimension) with positive cosmological constant. The reason for this is that it does not appear to be possible, with Lambda > 0, to define precise observables. This is natural if it is the case that a world with positive cosmological constant (like the one we may be living in) is always unstable.

If that is so, then a world with Lambda > 0 doesn't really make sense as an exact theory in its own right but (like an unstable particle) must be studied as part of a larger system.

Whether that is the right interpretation or not, since I don't know how to define any precise observables, I don't know what it would mean to try to solve 2+1-dimensional gravity with Lambda > 0, since it isn't clear what we'd want to compute.

==endquote==

Any comment?

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I thought that maybe Witten is going to merge String theory and LQG, that maybe he will cook up something like spin foam representation of String theory, this is what I wanted to ask for.So let's try to follow up on that theme. An influential string theorist is doing non-string gravity research. Is that part of a more general trend?

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marcus

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I don't expect that from Witten at all! But other people are working on stuff like that. There was posted just yesterday by Khavkine and Conrady.I thought that maybe Witten is going to merge String theory and LQG, that maybe he will cook up something like spin foam representation of String theory, this is what I wanted to ask for.

the nice thing when you use spinfoam methods is you can get a version of string-like object that does not require higher dimensions----the action happens in 4D or maybe 5D.

A string theory purist would not like this---maybe he would hate it---but some people find it interesting.

http://arxiv.org/abs/0706.3423

Florian Conrady (Penn State U.), Igor Khavkine (Western Ontario U.)

12 pages, 7 figures

(Submitted on 23 Jun 2007)

"We show that 3d SU(2) lattice Yang--Mills theory can be cast in the form of an exact string representation. The derivation starts from the exact dual (or spin foam) representation of the lattice gauge theory. We prove that every dual configuration (or spin foam) can be equivalently described as a self--avoiding worldsheet of strings on a framing of the lattice. Using this correspondence, we translate the partition function into a sum over closed worldsheets that are weighted with explicit amplitudes. The expectation value of two Polyakov loops with spin j becomes a sum over worldsheets that are bounded by 2j strings along a framing of the loops."

Also there are several papers by John Baez which get interesting results from string-like objects in 4D. Seeing Baez work one is tempted to ask: why bother with higher dimensions??!!

http://arxiv.org/find/gr-qc/1/au:+Baez_J/0/1/0/all/0/1

1. http://arxiv.org/gr-qc/0605087 [Broken] [ps, pdf, other]

Title:

Authors: John C. Baez, Alejandro Perez

Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)

2. http://arxiv.org/gr-qc/0603085 [Broken] [ps, pdf, other]

Title:

Authors: John C. Baez, Derek K. Wise, Alissa S. Crans

Comments: 41 pages, many figures. New version has minor corrections and clarifications, and some added references

Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Geometric Topology (math.GT)

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