Is 3D Quantum Gravity Equivalent to a TQFT?

In summary, there is still ongoing debate and uncertainty about whether quantum 3D BF theory is equivalent to quantum 3D gravity. While it is typically believed that in 3D it is BF theory and in 4D it is constrained BF theory, there is evidence that the 3D case may not be fully understood and resolved. Some sources suggest that the Ponzano-Regge model and the Turaev-Viro model may provide a proper regularization for the theory. However, as of 2009, the existence of quantum 3D gravity was still not known and the question remains unresolved."
  • #1
atyy
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I'd always assumed it was, since LQG spin foam models are based on BF theory. And it is typically said that in 3D it is BF, and in 4D constrained BF. The 4D quantum case is not known to be gravity, but I had thought the 3D case was.

Yet in http://math.ucr.edu/home/baez/week254.html Baez commentary on Witten's http://arxiv.org/abs/0706.3359 says "Even though Witten is now claiming 3d quantum gravity can't be a TQFT ...", which means the question was not resolved as of 2007.

Apprently, even the existence of quantum pure 3D gravity wasn't known in 2009 http://arxiv.org/abs/0906.1313 (see the fourth problem).

So is quantum 3D BF is quantum 3D gravity?

What is the status of this problem now?
 
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  • #2
I just remembered, isn't it supposed to naively be the Ponzano-Regge model, and properly regularized by the Turaev-Viro model? eg. http://arxiv.org/abs/0803.3319
 

1. What is 3D quantum gravity?

3D quantum gravity is a theoretical framework that attempts to merge the principles of quantum mechanics and general relativity in three-dimensional space. It is still a developing area of research and there is currently no universally accepted theory.

2. What is TQFT?

TQFT stands for topological quantum field theory, which is a mathematical framework used to study topological properties of a space. It is a type of quantum field theory that is independent of the metric or geometry of the space it is defined on.

3. How do 3D quantum gravity and TQFT relate?

There is currently no consensus on the exact relationship between 3D quantum gravity and TQFT. Some theories suggest that 3D quantum gravity may be a specific case of TQFT, while others propose that they are distinct theories that may have some overlapping concepts.

4. Is there evidence to support the idea of 3D quantum gravity as a TQFT?

At this time, there is no experimental evidence to support the idea of 3D quantum gravity as a TQFT. However, there have been mathematical studies and theoretical arguments that suggest a possible connection between the two theories.

5. What are the implications of 3D quantum gravity being a TQFT?

If 3D quantum gravity is proven to be a TQFT, it would have significant implications for our understanding of the fundamental laws of physics. It could potentially help bridge the gap between quantum mechanics and general relativity, and provide a more complete understanding of the universe at a fundamental level.

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