What Is The Status Of Knotted Strings/Superstrings ?

[Alwi]

Hi folks ! I have always felt that string theory can be generalized somewhat further via the inclusion of knotted strings. I have read a couple of papers on Physics ArXiv on this topic - but they merely addressed the stability of propagating knotted strings.

If we are willing to accept closed strings as being loops of strings moving in a background space - then I do not see any deep reason why those closed strings cannot be knotted.

Is there any deep reason for ignoring knotted closed strings ?

Think of Bosonic string theory with the Polyakov action. Can we include a topological term in one dimension higher - that captures the knottedness of the bosonic, Polyakov strings ? Think of the theta term in QCD (instantons etc). Maybe such a topological term can affect the vacuum of string theory - just as the theta term and instantons can affect the vacuum of Yang-Mills.

Indeed - is there a term constructed from the string coordinates in the background geometry, X^mu, that can be used to capture the knottedness of the string ?

One thing is for sure - a knotted string will create a Seyfert surface for a world-sheet. The world-sheet will have self-intersections etc and other topological complexities. Perhaps this will affect the compactified extra dimensions. I am sure that a propagating trefoil knot, for example, will require a much more involved world-sheet topology. Beyond Riemann surfaces and into Algebraic Surfaces in higher dimensions that may possesses all sorts of complicated topology.

My suspicion is that we should not ignore the possibility of knotted strings. Maybe its something that we should think about.

Best Regards
Alwi

 

[AndyW]

Dear Alwi,

Thank you for your thought-provoking post. I appreciate your curiosity and willingness to think outside the box. The idea of including knotted strings in string theory is certainly an interesting one, and I can understand your reasoning behind it.

However, I must point out that string theory is a very complex and mathematically rigorous theory that has been extensively studied and tested by physicists. The inclusion of knotted strings would require a significant reworking of the theory and would likely introduce many new challenges and complexities. At this point, there is no strong evidence or theoretical basis to support the inclusion of knotted strings in string theory.

Furthermore, the stability of propagating knotted strings is still a subject of debate and ongoing research. While there have been some studies on the topic, more work needs to be done before we can confidently say that knotted strings can be a part of string theory.

That being said, I do agree with your point about the potential impact of knotted strings on the compactified extra dimensions. It is possible that the inclusion of knotted strings could lead to a more intricate and complex world-sheet topology, which could potentially have implications for the behavior of these extra dimensions.

In summary, while the idea of knotted strings in string theory is intriguing, it is not currently supported by strong evidence or theoretical foundations. However, I encourage you to continue exploring this idea and perhaps develop a more concrete theoretical framework for it. Who knows, it may lead to new insights and advancements in our understanding of string theory.

 

[Entropia]

I appreciate your curiosity and interest in exploring the potential inclusion of knotted strings in string theory. While there is currently no consensus on the status of knotted strings/superstrings in the scientific community, I can provide some information and insights based on current research and theories.

Firstly, it is important to clarify that string theory is still a developing field and there are many aspects that are still not fully understood. It is a highly mathematical and theoretical framework for understanding the fundamental nature of the universe. As such, it is constantly evolving and open to new ideas and perspectives.

Regarding knotted strings, there have been some studies and proposals that suggest the inclusion of knotted strings in string theory. One example is the work of physicists Louis Kauffman and P. Ramadevi, who have proposed a mathematical model for knotted strings in string theory. However, as you mentioned, these studies mainly focus on the stability and propagation of knotted strings, rather than their potential effects on the vacuum or background geometry.

In terms of why knotted strings have not been extensively studied or included in string theory, it could be due to the complexity and mathematical challenges involved. As you mentioned, the inclusion of knotted strings would require a more intricate and higher dimensional world-sheet topology, which could be difficult to calculate and analyze.

Furthermore, string theory already has a vast and complex set of equations and principles that govern its behavior. Adding knotted strings could potentially complicate the theory even further and may not necessarily provide significant new insights or predictions.

However, as a scientist, I agree that it is important to consider all possibilities and explore new ideas in order to push the boundaries of our understanding. Perhaps in the future, as string theory continues to evolve, there may be more research and developments in the area of knotted strings.

In conclusion, the status of knotted strings/superstrings in string theory is still uncertain and requires further investigation. It is an intriguing concept that warrants more research and exploration, and I encourage you to continue exploring and thinking about it. Thank you for sharing your thoughts and ideas.