Is the Standard Model a M-theory?

[arivero]

M theory is an 11 dimensional theory which in some limits can reproduce all the five 10 dimensional string theories, and also 11D supergravity in some other limit. The mantra of string theory has been, for years, "we do not know what M-theory is".

On the other hand, 11 dimensional space is the minimal Kaluza Klein extension to reproduce the standard model group. This was noted time ago by Witten, the same person who took the effort of promoting M-theory.

Also, an string theory should be expected to emerge from the standard model in the limits where confinement appears; the string being the cause of the confinement. There are even some different limits to produce strings, depending on phases of the theory.

So I wonder, could it be possible to manipulate the parameters of the standard model in order to reproduce each of the five superstring theories?

 

[BenTheMan]

I don't know TOO much about M-theory, but I'm confused as to what you're talking about. To my knowledge, M-theory hasn't been shown to contain the standard model yet, which is a rather large research program in the US and in Europe. The best attempts that I know of are by Gordy Kane and collaborators.

So I'm confused by your question. Could you clarify?

 

[arivero]

I don't know TOO much about M-theory, but I'm confused as to what you're talking about. To my knowledge, M-theory hasn't been shown to contain the standard model yet, which is a rather large research program in the US and in Europe. The best attempts that I know of are by Gordy Kane and collaborators.

So I'm confused by your question. Could you clarify?

Yes. The usual lore is:
- that M-theory will contain the standard model in some subset of parameters.
- that M-theory will be some yet-to-be-discovered 11D theory whose limits are the usual 10D string theories.

What I was wondering is if, given that the standard model can be formulated as a 11 dimensional Kaluza Klein theory, could it be possible to use the different parameters of the standard model to find the 10D string theories.

 

[nrqed]

Yes. The usual lore is:
- that M-theory will contain the standard model in some subset of parameters.
- that M-theory will be some yet-to-be-discovered 11D theory whose limits are the usual 10D string theories.

What I was wondering is if, given that the standard model can be formulated as a 11 dimensional Kaluza Klein theory,

I am no expert on this but I had the impression that the standard model could not be formulated as a 11 dimensional KK theory.

Let's be clear about what we mean by "11 dimensional KK theory", however. When I hear this it seems to mean that all the forces would arise from compactification of gravity in 11 dimensions. But I think that's what Witten showed could not be done because no chiral force may arise this way (although Haelfix seems to have implied in a recent post that compactification techniques not covered in Witten's original paper could do the trick..I am not sure if I understoof correctly his/her post).

In any case, even in superstring theory, the gauge forces in 4 dimensions do NOT arise from compactification, a la Kaluza-Klein. Instead, one must have from the start a gauge theory in 10 dimensions. This was the first superstring revolution: the discovery that there was two (and only two) gauge group in 10D superstring theory that did not have chiral anomalies: SO(32) and E8 X E8.

So my point is that even in superstring theory the 4D gauge forces do not arise a la Kaluza-Klein.

 

[BenTheMan]

What I was wondering is if, given that the standard model can be formulated as a 11 dimensional Kaluza Klein theory, could it be possible to use the different parameters of the standard model to find the 10D string theories.

Well, the standard model is an effective field theory, so my guess is that this treatment would be not valid. I mean, presumably there isn't just ONE copy of the standard model in the string landscape, maybe there's 10. If there's ten, then those EFTs would all be the same (down to coupling constants and Yukawas), and they would be indistiguishable. The only way that we could distinguish the vacua is to probe things at the compactification scale.

Let's be clear about what we mean by "11 dimensional KK theory", however. When I hear this it seems to mean that all the forces would arise from compactification of gravity in 11 dimensions. But I think that's what Witten showed could not be done because no chiral force may arise this way (although Haelfix seems to have implied in a recent post that compactification techniques not covered in Witten's original paper could do the trick..I am not sure if I understoof correctly his/her post).

I think you can stick M Theory on a G2 manifold and get things that (in principle) LOOK like SM gauge groups and matter content. See papers by a guy named Bourjaily (very bright guy). But I know very little about this subject.

 

[arivero]

Well, the standard model is an effective field theory, so my guess is that this treatment would be not valid. I mean, presumably there isn't just ONE copy of the standard model in the string landscape, maybe there's 10.

Hmm perhaps the word "landscape" has been sort of abused... My understanding is that the M-theory span is a kind of parameter space which has the superstring theories as specific limit points here and there. And each point of these parameter space is a theory by itself, having its own landscape of compactified theories.

Now the tenant of string theory is that somewhere in the parameter space of, if you wish, M-theories, there is one special compactification which produces the world we observe, and then this special point of the landscape of this special theory contains the standard model.

And if we move in the parameter space of M-theories to reach some of their 10-dimensional limits, that spatial compactificacion will change too. In some limit it will dissapear, in some other it will have properties different to the ones of Nature, say massive gluons or massless electroweak bosons, or a couple more or less of particles. But we should expect to find some properties of the standard model in each of the known limits of M-theory.

Thus we should be able to do the process without knowing what M-theory is. We should have some way of doing limits in the standard model so that it becomes a point in the moduli space of each string theory, and dualities should relate these points.

 

[Coin]

The usual lore is: - that M-theory will contain the standard model in some subset of parameters.

Nitpick: Surely you mean not the Standard Model, but the MSSM? My understanding is that any parameterization of M-theory will always be supersymmetric.

 

[arivero]

Nitpick: Surely you mean not the Standard Model, but the MSSM? My understanding is that any parameterization of M-theory will always be supersymmetric.

Nitpick: of course, the MSSM contains the Standard Model. So if A contains B and B contains C...

(but honestly, if I preferred to speak of the standard model instead of the MSSM is because of my own exotic ideas about supersymmetry, known enough by the usual inhabitants of PF)

 

[Dcase]

Hi arivero,

I do not know the final answer to your question.

I think it is important to note that Edward Witten does have a background in economics and Morse Theory.

Somehow particles in the SM, MSSM or M-theory self-organized.

I have been reading dynamics and ergodic theory mathematical literature.
John Conway and Steven Wolfram work in cellular automata 37B15, within this general category 37-xx from AMS 2000 Mathematics Subject Classification
http://www.ams.org/msc/

There is this interesting arxiv paper:
Vladimir A. Manasson, 'Are Particles Self-Organized Systems?', 2008, 11 pages, 10 figures.
http://aps.arxiv.org/abs/0803.3300

 

[arivero]

When I hear this it seems to mean that all the forces would arise from compactification of gravity in 11 dimensions. But I think that's what Witten showed could not be done because no chiral force may arise this way

the more I read that paper, the less it seems to me a no-go paper. In fact, I'd say that a good part of the excitation of M-theory was about going back to 11d.

Said that, I am a bit worried about understanding how the extra dimensional stuff works. Take the simplest case, U(1)... does KK electromagnetism has a length scale? Or is it uncompact?

And generically... how is it that the number of dimensions does not match the number of generators of the gauge group? Is it telling that SymBreaking can not happen for all the generators of a group?

In any case, even in superstring theory, the gauge forces in 4 dimensions do NOT arise from compactification, a la Kaluza-Klein. Instead, one must have from the start a gauge theory in 10 dimensions. This was the first superstring revolution: the discovery that there was two (and only two) gauge group in 10D superstring theory that did not have chiral anomalies: SO(32) and E8 X E8.

Perhaps that SO(32) is overdimensioned. How do these groups transform under dualities?