Calibi-yau manifolds affecting the size of strings

[dhillonv10]

Hi all,

I am rather new here but I think I am posting in the right place, if not my apologies :) Alright so I've been working on calibi-yau manifolds for some time now and string theory (let's take a generic approach here and not worry about which version) states that the shape of the manifold precisely determines how the string will vibrate, so from following that, can I conclude that they also determine the size of the strings? It sounds logical to me, but does that make any sense? As a further extension of this, is it possible to change the size of the string by affecting the manifold itself? Has any work (research) been done regarding this? Generally we don't find the exact answer but someone variation thereof or sometimes the mechanism to solve one problem leads to solving another, I would very much appreciate if someone can offer me some guidance on this and possible links to papers. Thanks.

I do realize that the size is determine by coupling constants but to change the size, would I have to focus on the manifold itself or the constants?

 

[AndyW]

Hello,

Thank you for your question and for sharing your research interests with us. I am also a scientist and have some understanding of string theory and calabi-yau manifolds. To answer your question, yes, the shape of the manifold does play a crucial role in determining the size of the strings. In string theory, the strings are considered to be one-dimensional objects and their size is determined by the shape of the extra dimensions in which they vibrate. This is known as the compactification of the extra dimensions.

To change the size of the string, you would need to focus on the manifold itself. By altering the shape of the manifold, you can change the size of the extra dimensions and therefore affect the size of the string. However, it is not a straightforward process and requires a deep understanding of the mathematics of calabi-yau manifolds and string theory.

There has been some research done on this topic, specifically in the context of mirror symmetry. Mirror symmetry is a mathematical duality between two different calabi-yau manifolds, where the size of the extra dimensions can be changed while maintaining the same physics. This suggests that the size of the string can be altered by changing the shape of the manifold.

I would recommend looking into research papers on mirror symmetry and the work of physicists such as Brian Greene and Edward Witten. They have made significant contributions to understanding the relationship between calabi-yau manifolds and string theory.

I hope this helps guide your research and provides some insight into your question. Best of luck in your studies!