# The wrong turn of string theory: our world is SUSY at low energies

1. Jul 13, 2017

### arivero

I am doing a fast review of the bibliography; I'd say we have accumulated a lot. The main problem with the open string formulation is that there are two simultaneous bootstraps putting charges at the ends of the string: the one of the generation group, via supersymmetry, and the one of su(3), via (3 x 3)_anti = 3. They can not be independent because the 15 of SU(5) goes with the 3 of SU(3), whule the 24 goes with the singlet. Which amazingly could be compatible with a claim (hep-ph/9606467) that 54 and higher representations of SO(10) are always in the singlet of any other factors.

Half a 54, which we can do because it contains both particles and antiparticles, is a 27, and then the search scope becomes too wide. A traditional mention is (3,3,3) + (/3,/3,/3) of SU(3)^3, falling from E6 (but it is more typical to smash it into 16+10+1 of SO(10). In both cases, further breaking is needed if we want to get something close to the above decomposition)

Other 54 pathway, which can appear from branes too, is from the 55 of Sp(10), with only the nuissance of the extra singlet. The appendix of hep-th/0305069 mentions that this 55 could be obtained from orientifolds, but it doesn't give a reference. 1206.0819v2 suggest a realization with D7-branes. hep-th/0204023 Uses D7, D3 and O3 for generic Sp(2N+2M)xSp(2N), but does not evaluate our particular N=3 M=2. Neither do Luty et al hep-th/9603034v2 when looking at Sp(2N) susy. Similarly Witten 83 go for generic Sp(2N). This is an interesting paper even if if it focuses on its use as coloration.

A recent work arXiv:1603.05774v2 considers the "hidden pions" in the 15 both comming from SO(10) and Sp(10), and it proposes mass formulae! I do not get how it presents them as pions and not diquarks.

Also recently arXiv:1608.01675v1, Arkani-Hamed et al, mentions the decomposition from 15 into SU(5) with quantum numbers from the standard model. Comparing with this one, and with Vachaspati, it seems that the innovation here in this thread is the use of the most internal SU(3) for flavour instead of colour; the logic being that the string will take care of colour.

Googling for group decompositions, even with site:arxiv.org flag, is very inneficient, so sure I am missing important references.

Last edited: Jul 13, 2017
2. Jul 15, 2017

### arivero

I would like to find some strong -pun intended- argument to use SU(3) instead of any other SU(N), big N etc... Lacking this, it could be worthwhile to note that having a 54 and pasting an U(3) upon it is pretty interesting. It could be nice to have Lisi or Toni Smith or some other big numerologists here in the thread. On my side, lets at least notice that
$$54*9 = 496-1-9$$

Or,
$$\bf (15,3)+(15,6)+(15,3)+(15,6)+(24,8)+(24,1)+(1,8)+(1,1) \\ =45+90+45+90+192+24+8+1\\ =495$$

If this is a branching rule of something into something, I do not know. It looks so, but I am not conversant with large representations.

EDIT: from wikipedia https://en.wikipedia.org/wiki/Green–Schwarz_mechanism
A more modern analysis is quoted by Lubos here http://motls.blogspot.com/2010/07/string-universality-theres-no-u1496.html but no clue of where our representations comes from.

Last edited: Jul 15, 2017
3. Jul 16, 2017

### arivero

Actually I was thinking other two different venues to approach 496:
1. somehow expand SO(32) as a sum "SO(1+5+10+10+5+1) " and consider only the 10 for particle content. This way could be useful if colour is not invited to the party
2. promote each preon with a colour label, so the matrix is promoted from dim 10 to dim 30. Still, we need to add manually an extra preon/antipreon pair, uncolored, to get up so SO(32). This looks more natural that the previous post where we only have dim 30 and it is the 3x3 submatrices that overfill across the diagonal fo fill up to 495 "states".
Then, of course, both cases -and the previous one- need some argument to extract only the sm-like representations.

Last edited: Jul 16, 2017
4. Jul 18, 2017

### arivero

I am starting to suspect that special embeddings where not fully explored in the old age. Witten 84 does SO(32) to SU(5) via the most trivial way, times SO(22) and then not looking for generations nor colour (as it is already considered in the GUT group). Fortunately Gell-Mann, Ramond and Slansky look for colour too... but, uh, do they forgot the $(1, n^2_3 -1, 8^c)$ here?

Formula 2.18 for our case should decompose SO(32) as $$(n \times n)_A= [1,1,1^c] + {\bf (1,24,1^c) }+ (1,1,1^c) +(1,1,8^c) + (2,5,3^c) + (2,\bar 5, \bar 3^c) +{\bf [1,15,\bar3^c]} + {\bf [1, \bar {15}, 3^c]} +[1,10,6^c] + [1, \bar 10, \bar 6^c] + 1,24,8^c$$

For verification, it is possible to branch down to this same result using the new tables of
arxiv.org:1511.08771 via regular branching to $so30$ and $su15$, and then special branching down to $su15 \times su3$.
1. For so30 ⊕ u1(R):
• 496 = (435)(0) ⊕ (30)(2) ⊕ (30)(−2) ⊕ (1)(0)
2. Then for su15 ⊕ u1(R):
• 435 = (224)(0) ⊕ (105)(4) ⊕ (105)(−4) ⊕ (1)(0)
• 30 = (15)(2) ⊕ (15)(−2)
3. and then ⊃ su5 ⊕ su3(S):
• 224 = (24, 8) ⊕ (24, 1) ⊕ (1, 8)
• 105 = (15, 3) ⊕ (10, 6)
• 15 = (5, 3)
• (and none from 120 = (15, 6) ⊕ (10, 3) )
Perhaps some way down via so12⊕ su3(S), and so12 is so(2)xso(10) and then so(2)xsu(5)? Also, perhaps O(n) and U(n) instead of su, so?

I am not sure if this is the right branching, or it is the former one, or
some other, but I find a bit disappointing that the final conclusion
of this thread is going to be to identify the lost scalar partners as bosons of the SO(32) string. Such
idea should already be in the literature somewhere.

Last edited: Jul 18, 2017
5. Jul 18, 2017

### mitchell porter

I have been worried all week that you are too optimistically jumping between flavor symmetries and gauge symmetries. For example, that scalar 54 which is supposed to come from the mesons and scalar diquarks of five quark flavors, assumes an SO(10) flavor symmetry, which is rather unusual. But in most of this week's rampage through representation theory, you've been looking at gauge groups, not flavor groups.

As you say, Gell-Mann et al is good because they are looking at flavor and color together. So we have at least one clear example of how to do that. But there are further twists. When the theory is strongly coupled, there may be chiral symmetry breaking that reduces the flavor group, and determining that is an art in itself. (It's very very likely that this is related to the sBootstrap, since the pions are precisely the Goldstone bosons of chiral symmetry breaking.)

Also, "there are no global symmetries in string theory". There is a worldsheet theorem that if a global symmetry exists, there must be a corresponding gauge-boson state of the string, turning it into a local symmetry. In Sakai and Sugimoto's holographic QCD, flavor is gauged. But it's also possible for the global symmetry to just be approximate. There is some discussion here.

6. Jul 19, 2017

### mitchell porter

I have just run across two highly relevant papers by Armoni - 1310.2027 and 1310.3653. They came out near the start of this thread's long dormant period, from late 2013 through all of 2014... The first one, in particular, is remarkable for how many of our themes it contains.

I'll set the scene with a remark from that first paper (page 7). We are dealing with a field theory which is realized in string theory by a "Hanany-Witten" brane configuration "identical to the brane configuration that realizes SO(2N) SQCD, except that the D4-branes are replaced by anti D4-branes".

I'm emphasizing this because, if we do have to study this one in detail, we know that the place to begin is with the configuration that realizes SO(2N) SQCD. Armoni is interested in a similar but non-supersymmetric theory; but it may be that we will want to go back to the supersymmetric prototype.

Another thing to note is that these Hanany-Witten configurations can be lifted to M-theory. In Type II theories, they appear as a web of D-branes and NS-branes (and in this case, an orientifold plane), but in M-theory, they can be realized as a single M5-brane, on the right geometric background.

Armoni is concerned with two field theories, an electric theory and a magnetic theory. He is proposing a Seiberg duality. Inter-brane forces which cause the branes to rearrange themselves are also a part of it.

What I want to note here, are the symmetries and some of the particle content. The flavor symmetry is SO(2Nf). There are particles in the non-supersymmetric theory (but which is, remember, descended from a supersymmetric theory) which he calls quarks, squarks, a gluino, a meson, and a mesino. The gluino transforms in an antisymmetric two-index representation of the gauge group, so it might be a toss-up as to whether the gluino or the squarks are more like diquarks.

On page 18, the breaking chain SU(2Nf) -> SO(2Nf) -> U(Nf) is referenced. And the companion paper talks about chiral symmetry breaking.

7. Jul 24, 2017 at 11:07 AM

### arivero

The next temptation is to try to classify under chirality those bosons we have got in a 496 (or 495 or whatever), or the original 54 ones. If we assume that they were produced, in SO(10), via a set of five "quark preons" and "five antiquarks", then the next step is again obvious: consider sum and difference of particle-antiparticle, as such is the way to build chirality invariant states, and see what happens with the group? Does it decompose to a product of two groups, one for left, other for right chiral? And when we scale up, what does happen? Does 496 divides in 248+248, or 495 in 1+247+247 ?

(amusingly #247 is the number of this post in the thread... yes, numerology is always a running joke here :-)

Last edited: Jul 24, 2017 at 11:31 AM
8. Jul 25, 2017 at 5:36 PM