Electric and Color charge in String Theory

[Spinnor]

I get a gist of how electric charge comes about in string theory here,

https://physics.stackexchange.com/questions/5665/electric-charge-in-string-theory

How much needs to be amended to the above answer to understand how color charge comes about in string theory? I assume there are interesting similarities and differences between how electric and color charge are understood in string theory.

Thanks for any help!

 

[Spinnor]

An understanding of this image might help? From, http://www.diffusion.ens.fr/vip/pageJ03.html

 

[arivero]

It is very interesting that you ask for electric + colour, and not electroweak.

 

[Spinnor]

It is very interesting that you ask for electric + colour, and not electroweak.

How wrong is it to think of the electromagnetic force as a force separate form the weak interaction? I know they are unified but the weak force just makes things more complicated and real. I have been meaning to learn more about the electroweak force guess the time is tonight.

So if electric charge can be roughly thought of as momentum in some compact space can the other charges be roughly thought of as momentum in a compact space in different directions from in our compact space?

Thanks!

 

[arivero]

How wrong is it to think of the electromagnetic force as a force separate form the weak interaction? I know they are unified but the weak force just makes things more complicated and real. I have been meaning to learn more about the electroweak force guess the time is tonight.

Plus, a lot of string theory is about limit cases, so surely it is reasonable to think also of the standard model in a limit case, EM+colour. The only proviso is that even in such limit some mechanism should exist to connect with the full SM content.

 

[mitchell porter]

This could be a very long thread, for several reasons. Witten http://www.sns.ias.edu/ckfinder/userfiles/files/%5B52%5DProc_Shelter_Is_II_1983.pdf: "As soon as one begins to think about Kaluza-Klein theory, one faces a bewildering variety of choices. There are many assumptions one might make, and many facts about elementary particle physics one might try to explain." (And he said that before modern string theory, with its googolesque landscape of vacua, was developed!) To this I would add that decades of study of KK theories has produced a vast body of theoretical knowledge. We may not know which KK theory, if any, describes reality, but a large number of possibilities have been studied, and it's not obvious which paths one should mention.

The question refers to string theory, but string phenomenology, the application of string theory to the real world, does not employ extra dimensions in the way that old Kaluza-Klein theory did. As discussed in this thread, the old KK theory obtains gauge fields from a kind of symmetry of the extra dimensions (continuous isometries) that the spaces now used in string phenomenology (e.g. Calabi-Yau manifolds) do not even possess. In the old KK theory, gravity is fundamental and the gauge fields actually result from gravity in the compact extra dimensions. In string phenomenology, one either starts with a big gauge symmetry that is just as fundamental as gravity (e.g. E8 x E8 in the most popular heterotic theory), which is then broken to something simpler by compactification; or one has gauge groups arising from the open strings attached to stacks of branes (as illustrated in comment #2 in this thread).

The old KK option still exists in string theory, and has been studied, but not for phenomenology, not for the purpose of directly describing the real world. Instead, it has been a way to learn more about the properties of the theory, how strings work. I know @arivero to be interested in the possibility that the old-style KK mechanism could be applied within string phenomenology, and he has some interesting concrete ideas. So we may want to discuss that, along with, or even instead of, a review of how conventional string phenomenology works. After all, we do not at all know the limits of string theory, and we don't know that the way it is being applied now is on the right path.

We should probably also visit the field theory of electric and color charge, i.e. what "charge" means for the different cases of U(1) and SU(3). Mathematically it refers to a type of "representation" of the symmetry group. But where the representations of U(1) are indexed by real numbers - thus, the usual notion of electric charge - the representations of a group like SU(3) are instead vector spaces classified by dimension and by the action of the group on the vectors. So regarding the specific question

if electric charge can be roughly thought of as momentum in some compact space can the other charges be roughly thought of as momentum in a compact space in different directions from in our compact space?

I actually doubt that it can be thought of in that way. (Also, representing U(1) charge as a momentum in the fifth dimension has its own difficulties when applied to the real world, which I briefly mentioned in comment #2 here.) I think that, in an old-style KK theory of nonabelian gauge fields like SU(2) or SU(3), in the higher-dimensional description, the particles with weak charge or color charge would just be a many-component unified "spinor" field interacting with the gravitational field. However, there is actually a classical description of such interactions, called Yang-Mills-Wong theory, that you might want to look up.

 

[Spinnor]

View attachment 211624 An understanding of this image might help? From, http://www.diffusion.ens.fr/vip/pageJ03.html

Various aspects of the above image are explaned here,

http://web.mit.edu/physics/news/physicsatmit/physicsatmit_04_vibratingstrings.pdf

 

[mitchell porter]

This is one of the easier kinds of string model to understand... There is a famous kind of illustration of extra dimensions (e.g. see bottom picture on this page) which shows a grid with a gnarly shape located at each point of the grid. The grid stands for 3+1 dimensional space-time, each gnarly shape stands for the extra dimensions at that point. You should imagine this web of branes-connected-by-strings, as the gnarly shape present at each point of the macroscopic space-time. A particle - let's say an electron - is a particular type of string (in the diagram, it would be one of the "lepton" strings), and an electron traveling through 3+1 space, is an electron-string maintaining its location in the brane-web, but moving along the grid.

There are many elegant aspects to how this works. Each brane stack carries a gauge field. Strings within the stack are the gauge bosons, strings between two stacks are charged under both gauge groups because they can interact at their ends with the gauge bosons. The strength of the gauge coupling depends on the volume of the branes. The massive Higgs comes from a gap in one of the stacks; the yukawa interaction which gives fermions mass, is a three-way interaction with the Higgs string whose strength depends on the surface area traced by the strings. The branes, and the dimensions containing them, are dynamical, and their lowest-energy configuration determines all these areas and volumes that in turn determine the parameters of the standard model.

When you look further at the details, then you get some complications. That picture is only telling you how the branes intersect and what they mean physically. The actual geometry of the brane stacks is hard to visualize - intersecting three-dimensional objects in a six-dimensional space. Also, it's actually an orbifold space, one that has been "divided by a reflection". Also, all those strings are superstrings, so that e.g. each "quark-string" actually has a quark mode and a squark mode. Worst of all, for a typical model, no-one can actually calculate the lowest-energy configuration of the brane geometry! So we can't extract the predicted values of SM parameters that should be implied by a specific choice of geometry.

 

[Spinnor]

Worst of all, for a typical model, no-one can actually calculate the lowest-energy configuration of the brane geometry! So we can't extract the predicted values of SM parameters that should be implied by a specific choice of geometry.

Job security for string theorists!

Thank you!