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Alex, adv. diab.'s Avatar Jump to comment 48 by Alex, adv. diab.

Comment 47 by Anaximander :

Grab a pencil and do the following: Draw a triangle one side of which consists of 5 parallel lines really close to each other, one side of 2 lines, and the third side of only one single line. Congratulations, you have constructed a SU(5) x SU(2) x U(1) x... intersecting brane model in Type IIA superstring theory :D Those lines schematically stand for 7-dimensional membranes which extend to our 4 dimensions, and three of the six additional ones. The geometry of the 6 extra dimensions must then be chosen such that it can accomodate these membranes (they somehow must be wrapped up onto themselves since the extra dimensions are only finitely large).

Of course. Now we need to understand how (and how fast) the transitions between that and the other possible structures happen. How do these change the expansion rate of space? Will they leave some marks on the CMB radiation?

I have no clue at all what the tunneling rates between topologies would be. I would dare to suggest that at high temperatures, all these topologies would fluctuate to and fro, and we should thus try to calculate differential probabilities. Also, if they leave a trace anywhere in our current data, it would be the CMB. However, it is as of now unclear how inflation would have to be implemented in string theory (although there are many proposals), and this would probably be the dominant effect. So, to conclude, I don't know, and I don't know whether anyone knows :)

Tue, 29 May 2012 21:38:59 UTC | #944320

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Alex, adv. diab.'s Avatar Jump to comment 46 by Alex, adv. diab.

Comment 43 by Anaximander :

Now we have to combine these things. What would the shape of extra dimensions be, if the symmetry group in the atomic level is SU(3), SU(4) or SU(5)?

Grab a pencil and do the following: Draw a triangle one side of which consists of 5 parallel lines really close to each other, one side of 2 lines, and the third side of only one single line. Congratulations, you have constructed a SU(5) x SU(2) x U(1) x... intersecting brane model in Type IIA superstring theory :D Those lines schematically stand for 7-dimensional membranes which extend to our 4 dimensions, and three of the six additional ones. The geometry of the 6 extra dimensions must then be chosen such that it can accomodate these membranes (they somehow must be wrapped up onto themselves since the extra dimensions are only finitely large). This is a nontrivial task that cannot be put in simple words, but the structure of the subatomic interactions is already determined largely by the picture you've drawn. The quarks and leptons then are strings that are local to the interstection points (corners of the triangle), they start on one of these stacks of lines and end on the other. Simple, eh? :)

Are these shapes then so stable, that there would be time for life to exist?

This is a valid concern, getting the 6 extra dimensions in superstring models to remain stable at cosmological times without either blowing up or collapsing, is notoriously difficult and constitutes the central problem for string theorists today.

Fri, 25 May 2012 09:37:41 UTC | #943445

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Alex, adv. diab.'s Avatar Jump to comment 45 by Alex, adv. diab.

There are several formulations of superstring theory which in principle should all be equivalent, but in their manageable and calculable versions manifest themselves rather differently.

In the very popular so-called Heterotic E superstring model, going from 3 colors to 5 colors might be a problem since we are limited to the E_8 group as the total unified group of our so-called "visible sector" of ordinary matter, and having to spare a bigger part of it for the strong interactions would limit the types of interactions that are possible. That might or might not be a problem, i.e. the devil will probably be in details such as: ok I have my strong interaction with 5 colors, and all the quarks and leptons and Higgs bosons, but can I give the particles masses that lead to stable chemistry? Maybe one can coopt part of the so-called "hidden" sector interactions of the theory which are usually not included in realizing the Standard Model, to compensate.

In the so-called type II superstring theory, going to 5 colors seems to be comparatively trivial as well, since there, the number of colors corresponds to the number of higher-dimensional membranes which are stacked on top of each other. One could simply use the know-how from constructions of SU(5) unified theories and add some stuff for the electroweak interactions. The string theorist whom I just annoyed with this question says that it's no harder than three colors on a technical level. Caveats from above also apply.

Fri, 25 May 2012 09:19:00 UTC | #943443

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Alex, adv. diab.'s Avatar Jump to comment 42 by Alex, adv. diab.

This really is a fun question... So if you leave the standard model as it is and only crank up the number of colors, this would require the electric charges of the quarks to change in order to get rid of the anomalies. So for SU(5), the charges of the up and down quarks would have to be (1/10) +/- (1/2) rather than (1/6) +/- (1/2) as is the case in nature. Then the nucleons which would contain five quarks would have a fun variety of electrical charges. It is a rather subtle thing that in our world, neutrons are stable within atomic nuclei (they decay to protons in about 15 minutes outside of a nucleus). So before we are even able to ask questions about star lifetimes, we would have to clarify whether we even have stable atomic nuclei, and what they would look like. It would for example be possible that rather than two different nucleons than can be stable within a nucleus, there are four,

uuuud, uuudd, uuddd, udddd

with charges 2,1,0,-1,

or only one of them... One would have to estimate the masses of these states. It is possible that for symmetry reasons the two inner ones have similar mass, and the two outer ones. At least the anomaly condition would ensure that nuclei have integer charge which can be neutralised by electrons in the hull as long as the net charge is positive, but interestingly, there would be combinations where the nucleus itself is neutral

Fri, 25 May 2012 07:00:53 UTC | #943431

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Alex, adv. diab.'s Avatar Jump to comment 34 by Alex, adv. diab.

Comment 21 by Anaximander :

Why, for example, does the strong force between quarks have an SU(3) summary as opposed to, say, an SU(4) symmetry?

Because then it would not be "the strong force." (It would be, for example, "the very strong force.")

Or maybe there would not be anybody to ask that, if it had SU(4) symmetry?

If the strong force were governed by SU(4), there would not be protons and neutrons as we know them since stable baryons then would have to contain 4 quarks instead of 3 (the relation indeed is that simple) and thus would be bosons instead of fermions. This would probably have had profound impact on the prospect for complex life (what does nuclear physics look like in the case of bosonic nucleons? Are there even differnet kinds of stable nucleons available with suitable electric charges that make stable nuclei possible?) . If you go to SU(5), there are again fermionic bound states, but they contain 5 quarks. I haven't thought about it, especially how efficiently such big bound states would have been created after the big bang, but it could be a deal breaker.

Thu, 24 May 2012 11:48:02 UTC | #943256

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