How to compute Physical Constants from given Calabi-Yau Compactification of Effective Field Theory of corresponding String Theory?

Question

I got some interest in String Theory when I was listening to lectures of David Tong and Brian Greene. I remember them stating that the spacetime manifold is compactified to resemble our usual 3+1 dimensions, using Calabi Yau Manifolds. But String Theory offers a lot of different possibilities of Calabi - Yau Manifolds one of which may resemble our universe.
And the other point is, if we let the strings(particles) vibrate in a particular manifold, we can essentially compute the physical constant related to it.
So, my question is, can I have resources like reviews, textbooks and any other resources related to this which will help me compute the physical constants from a given Calabi-Yau Manifold?
My Background: I know QFT in the level of Peskin. I know General Topology and Differential Geometry to some extent(I have taken a course in General Relativity, equivalent to Eric Poisson's lectures here)
Addendum:
I don't know how to compute constants from a manifold, I also don't know how those manifolds are represented(metric or connections??). I also don't know how much math is required as a prerequisite. I would be glad if you can share me with a roadmap to reach the above state.

Ramiro Hum-Sah · Answer

The question is broater. It strongly depends on what exactly you want to compute and from what string theory you want to obtain it.
General comments:

The best resource on general grounds is the book "String Theory and Particle Physics: An Introduction to String Phenomenology" written by Ibáñez and Uranga. There you can learn precise relations between the geometry of extra dimensions and the physical parameters of a given compactification.

Arguably "the basic" aspects of a compactifiction are: The spectrum of massless fields, Yukawa Couplings, the number of fermion generations and low energy gauge symmetries. The first aspect is captured by the cohomology of the internal space, the second ones are computed as intersection numbers, the third one is escencially (half) the Euler characteristic and the last one is understood via characteristic classes on the internal geometry. To learn about that, I recommend the book: "Calabi-Yau Manifolds: A Bestiary For Physicists". Warning: This book is excellent to understand in deep the geometry and the principles involved, but it's not the option if you are interested in specific phenomenological scenarios, realistic scenarios or "modern" setups involving fluxes or non perturbative effects.

Specifics:

If you have some string theory and CFT background, I strongly encourage you to read chapters 9 and 10 in Kiritsis book "String Theory in a Nutshell" for a concise and practical exposure to detailed phenomenological computations. Examples, excercises and references given are all excellent, beautiful and relevant for current research. If you want to learn how to compute physical parameters and its loop corrections, those chapters are a wonderful resource.

For the F-theory perspective I recommend: GUTs and Exceptional Branes in F-theory - I and GUTs and Exceptional Branes in F-theory - II

How to compute Physical Constants from given Calabi-Yau Compactification of Effective Field Theory of corresponding String Theory?

One Answer

Add your own answers!

Ask a Question