Freidel, Krasnov and Livine hints of Sring Theory in LQG

In summary, the conversation discusses a formula for the inner product in a specific space, which is expressed as a holomorphic integral over the space of "shapes". The integration kernel is related to the n-point function of the bulk/boundary dualities of string theory, giving it an interpretation in relation to the Kahler potential on the space of "shapes". The conversation also mentions a blog post and Wiki page that provide helpful visual explanations of the topic.
  • #1
MTd2
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http://arxiv.org/abs/0905.3627

At VIII. Disscussion, p. 36:

"Our main result is the formula (53) for the inner product in Hj1,...,jn in terms of a holomorphic integral over the space of “shapes” parametrized by the cross-ratio coordinates Zi. In the “tetrahedral” n = 4 case there is a single cross-ratio Z. Somewhat unexpectedly, we have found that the integration kernel ˆK (Zi, ¯ Zi) is given by the n-point function of the bulk/boundary dualities of string theory , and this fact allowed to give to ˆK (Zi, ¯ Zi) an interpretation that related them to the Kahler potential on the space of “shapes”."
 
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  • #2


I hope there will be discussion on this paper.
I need the help in trying to understand the math.

I put it into my blog at “How do I visualize particles?
https://www.physicsforums.com/blog.php?b=513 [Broken]

Wiki has some good visual explanations of 4-simplex and tetrahedron.
A picture is worth a thousand word!
jal
 
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  • #3


I find the work presented by Freidel, Krasnov, and Livine to be highly interesting and potentially groundbreaking. The use of loop quantum gravity (LQG) to explore hints of string theory is a novel approach that may lead to new insights and connections between these two theories. The authors' main result, the formula for the inner product in Hj1,...,jn in terms of a holomorphic integral over the space of "shapes," is a significant contribution to the field and has potential implications for our understanding of both LQG and string theory.

One particularly intriguing aspect of this work is the unexpected connection between the integration kernel and the n-point function of the bulk/boundary dualities in string theory. This suggests a deeper relationship between LQG and string theory than previously thought, and may open up new avenues for research and exploration.

Furthermore, the interpretation of the integration kernel as related to the Kahler potential on the space of "shapes" is a valuable contribution to our understanding of the mathematical structure underlying these theories. This sheds light on the potential geometric and topological aspects of LQG and string theory, and may provide a new perspective on how these theories can be unified.

Overall, the hints of string theory found in LQG by Freidel, Krasnov, and Livine are a significant step towards a more comprehensive understanding of these two fundamental theories. Their work has the potential to advance our knowledge and pave the way for further research in this exciting and rapidly evolving field.
 
  • #4


The authors of this paper, Freidel, Krasnov, and Livine, have presented an interesting and unexpected result in their study of loop quantum gravity (LQG). They have discovered a formula for the inner product in a particular space of states, Hj1,...,jn, which is described in terms of a holomorphic integral over the space of "shapes" parametrized by cross-ratio coordinates. What is particularly intriguing is that in the case of n = 4, there is a single cross-ratio Z, and the integration kernel ˆK (Zi, ¯ Zi) is related to the n-point function of bulk/boundary dualities in string theory. This suggests a connection between LQG and string theory, and the authors have provided an interpretation of the integration kernel in terms of the Kahler potential on the space of "shapes". This is a significant result as it provides a potential bridge between two major theories in theoretical physics. Further research and exploration of this connection could potentially lead to a deeper understanding of both LQG and string theory.
 

What is the connection between Freidel, Krasnov and Livine hints and String Theory in LQG?

The connection lies in the search for a theory that unifies quantum mechanics and general relativity. Freidel, Krasnov, and Livine have proposed a reformulation of loop quantum gravity (LQG) using the techniques of string field theory, which has the potential to provide a framework for this unification.

What is the significance of the hints of String Theory in LQG?

If successful, the hints of String Theory in LQG could provide a more complete understanding of the fundamental forces of nature, including gravity, and potentially resolve some of the incompatibilities between quantum mechanics and general relativity.

What are some of the challenges in applying String Theory to LQG?

One of the main challenges is that LQG is a background-independent theory, meaning that it does not rely on a fixed spacetime background. However, string theory is typically formulated on a fixed background, so reconciling these two approaches is a difficult task. Another challenge is the lack of experimental evidence for string theory, making it difficult to test its predictions in the context of LQG.

How does the use of String Theory in LQG differ from traditional approaches to quantum gravity?

Traditional approaches to quantum gravity, such as LQG, attempt to quantize gravity by treating it as a discrete, quantized field. However, string theory takes a different approach by treating gravity as a manifestation of the fundamental properties of strings. This allows for the possibility of a more complete unification with other fundamental forces.

What are some potential implications of successfully incorporating String Theory into LQG?

If successful, this could lead to a more complete and unified understanding of the fundamental forces of nature. It could also have practical applications, such as helping to resolve the paradoxes of black hole physics and potentially leading to the development of new technologies. Additionally, it could provide new insights into the nature of space and time, and potentially even the origins of the universe.

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