Can Kaluza-Klein theory accommodate magnetic charge?

[Spinnor]

Can Kaluza-Klein theory accommodate magnetic charge? If so is there a simple geometric difference between electric and magnetic charge in such a theory?

Thanks!

 

[Spinnor]

So if you can believe Professor Gary Horowitz the answer is yes and the geometrical picture is,

From,

Microstates of Kaluza-Klein Black Holes

From Google,

https://www.google.com/search?q=kal...webhp&ei=5c-UV7LqEsP--AGT8ZLICg&start=10&sa=N

Not sure what topological twisting of S^1 means?

Thanks!

 

[Spinnor]

Not sure what topological twisting of S^1 means?

I will take a stab at this. So we have a circle at each point of Minkowski space, S^1. Say at the origin we have magnetic charge. Suppose we now make one full orbit of this charge in the plane z = 0. Suppose that when we come back to where we started in the z = 0 plane in the compact space we have advanced or retarded by one full turn in the space S^1? Is that what topological twisting of S^1 means?

The magnetic charge is the topological twisting?

There is something else we could do. Suppose we take the circular fibers, give them a cut and then glue the ends at different points of our base space, let each pair of ends of all the circles be separated by the same small spacetime vector? Once around the fiber and we do not come back to where we started in space or even time. Is that an operation that gives a topological twisting of S^1?

Thanks!

 

[JorisL]

I'm not sure what topological twisting of a circle means.
This might be a good starting point http://www.itp.ac.cn/~gaoyh/doc/tt1.pdf (I'll try to have a detailed look at this tomorrow)

The following statement is fishy though

Say at the origin we have magnetic charge.

You want the resulting space (4D Minkowski) to behave as if it were cosmological in nature i.e. you cannot choose a unique point to represent the origin.
It would be like saying that the Earth's position is special compared to the rest of the universe.

If we allow such an origin it would be hard to talk about "our physics" unless I'm attributing too much importance to isotropy/homogeneity.

 

[Spinnor]

The following statement is fishy though

I was not clear then. I am suggesting that we look at the space surrounding a point magnetic charge and for simplicity let us place it at the origin of some coordinate system, just as we could place a point charge at the origin. There are only so many ways one can topologically twist the fibers S^1?

( And there has to be a whole lot of symmetry in the twisting of the fibers S^1, the symmetry of a point magnetic charge?)

Thanks for the link!

 

[Spinnor]

The following link is deeper then I hoped but does discuss magnetic monopoles and twisted fiber bundles together. Seems like there must be a more simple explanation?

https://golem.ph.utexas.edu/category/2008/04/magnetic_charge_anomalies.html

 

[Spinnor]

Another link, from Chen Ning Yang,

MONOPOLES AND FIBER BUNDLES Chen Ning Yang State

It has to be more simple then the above.

Starting at page 5 of the link below maybe getting simpler,

http://www.math.columbia.edu/~ums/pdf/Scaletta LecNotes UMS 2-3-10.pdf

 

[Spinnor]

That raises a question, what is the lowest dimension Kaluza Klein theory that magnetic charge can exist? Can one assume that magnetic charge is still a topological twisting of S^1?

Thanks!

 

[ohwilleke]

If Kaluza Klein did allow magnetic charge, that would be an argument against the theory (as no such thing is observed in Nature) rather than a point in its favor.

 

[Spinnor]

If Kaluza Klein did allow magnetic charge, that would be an argument against the theory (as no such thing is observed in Nature) rather than a point in its favor.

But the theory apparently does have room for magnetic charge, which is cool.

Do you by chance know what is meant by a "topological twisting" of the fibers S^1?

Thanks!