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

1. Mar 24, 2017

### mitchell porter

Following the previous post, I believe I really have identified the first genuine field-theoretic toy model of the sbootstrap - or at least, toy model of a crucial element of the sbootstrap. The field theory is just N=1 SQCD with Nc=2 and Nf=5. There is no electromagnetic charge, so this is not yet a model of the combinatorial aspect of the sbootstrap. But what it does give us, is a definite realization of the concept of "fermionic superpartners of pions and diquarks".

It's because of the fact, pointed out by Shifman and Vainshtein, that for SU(2)c, diquarks, like pions, are goldstone bosons. So in the N=1 theory, they will have superpartners that are goldstinos, goldstone fermions. For SU(3)c, the nature of diquarks is less clear. But as S & V argue (pages 6 & 7): "As we pass to SU(3)color , the exact symmetry no longer holds, but an approximate similarity in the spatial structure of pions and diquarks is expected to hold". They propose a way to formally investigate this, by adding a triplet Higgs to SU(3)c QCD which breaks it to SU(2)c. A similar procedure should be possible for SU(3)c SQCD.

It has been proposed before that the SM fermions are goldstinos. Here it seems we have to look for something a little more complicated - perhaps "almost-goldstinos" in the "magnetic theory" of a Seiberg duality.

2. Apr 17, 2017

### mitchell porter

In a 1984 paper, "Split Light Composite Supermultiplets", one generation of leptons is obtained from SQCD with three colors and three flavors. Furthermore, the preons have quark-like hypercharges (see equations 3.15). The leptons are obtained at equation 3.42. Those "χ"s are components of the superfield T, defined in equation 3.18. If I am interpreting that correctly, T is a product of a quark and a squark.

3. Apr 17, 2017

### mitchell porter

This was wrong, $\Phi, \tilde \Phi$ are chiral superfields in $3, \bar 3$ reps of SU(3) (see e.g. the start of section 3), so T is a meson superfield.

4. Apr 17, 2017

### ftr

Mitchell, why are you trying to figure out the proton, some people already got the noble prize for it, right.

5. May 7, 2017

### mitchell porter

Masiero & Veneziano 1984 provides a context in which e.g. a muon-pion superfield can be explored. But what about the quark-diquark relationship? An appealing possibility is that the next step beyond Shifman & Vainshtein 2005 is to work in N=2 supersymmetry. Seiberg and Witten analyzed the space of ground states for N=2 SU(2) gauge theory, and found that there were paths through it, in which composite objects (monopoles) map smoothly to elementary objects. The quark-diquark part of the sbootstrap has always looked like a kind of self-duality, and N=2 SU(2) SQCD may provide a context in which a change of variables can map a diquark superfield onto a quark superfield. (And to include charge, one would just work with U(n) rather than SU(n).)

6. May 8, 2017

### arivero

Hmm, it has been some years, so ok lets go for a recap :-)

Topic here was generically if String Theory had gone wrong turn at some moment, and particularly if it could be possible that it still does better for the pionic string. The observation for this particular is that one could consider a scenary where supersymmetry is not broken:

or a midly broken scenary

Both of them have the peculiar characteristic that the scalars are composites of the light quarks, or perhaps open strings terminated in such quarks. From here a lot of the discussion in the thread has become about accummulating research that could be related to quark - diquark or lepton-meson symmetries.

7. May 9, 2017

### oquen

Please tell me. Is the supersymmetric particle corresponding to dark matter stable? If it's not stable and can only be produced at laboratory.. how can they exist as dark matter that is always present?

8. May 15, 2017

### mitchell porter

That is a standard idea, yes. But the focus in this thread is on the unusual possibility that there are supersymmetric relations among the already known particles. Dark matter is a separate question, and could be anything.

9. Jun 14, 2017

### mitchell porter

A new paper compels me to correct some terminology from #221. I wrote as if the goldstone fermions I am interested in (as a realization of the sbootstrap) are goldstinos, but this is not so.

According to the Goldstone theorem, the spontaneous breaking of a continuous symmetry leads to a new particle, a Goldstone particle. Chiral symmetry breaking leads to pions, electroweak symmetry breaking leads to the Higgs boson and the spin-0 components of the W and Z.

All those examples are bosons. However, when supersymmetry is spontaneously broken, the emergent particle is a fermion. This is the goldstino.

The fermions I am talking about are not goldstinos and do not arise from the breaking of supersymmetry. Instead, they are the superpartners of Goldstone bosons like pions, that arise from the breaking of other symmetries.

(The new paper really does try to obtain SM fermions from goldstinos. But because you only get one goldstino per susy generator, to explain many or all of the SM fermions this way, it has to contemplate extended supersymmetries far beyond the usual N=8 limit.)

I will also note the existence of some papers trying to embed one of the classic Goldstone-fermion models of the SM (Kugo-Yanagida model) into string theory. The methods employed may be useful if we do find a sigma model that convincingly implements a sbootstrap-like relation.

10. Jun 14, 2017

### arivero

32 pages on how Thomson might have discovered supersymmetry

11. Jun 23, 2017

### arivero

Revisiting the question of connection between the sBootstrap and the waterfall, let me put the waterfall mass levels into the sBootstrap-inspired arrangement of fermions, mesons and diquarks. The first column is the fit to zero and 174.2 GeV, and the second colum is the "rotated" calculation where the sum of the three main levels is fit by asking it to be exactly three times the sum of the original koide triple for leptons (so electron + mu + tau).

$$\begin{array}{|rr||l|l|llll||} \hline 174200 & 173260 & \\ 3640 &4197.57 & \stackrel{\bar c\bar c}{cc}& \nu_2, b_{rgb}, e, u_{rgb}& B^\pm,B_c^\pm & \stackrel{\bar b\bar u}{bu}, \stackrel{\bar b\bar c}{bc} & \stackrel{\bar b \bar s}{bs}, \stackrel{\bar b\bar s}{bd} & B^0, B^0_c, \bar B^0, \bar B^0_c \\ 1698&1359.56 & \stackrel{\bar c\bar u}{cu}& \tau, c_{rgb} , \nu_3, d_{rgb}& D^\pm, D_s^\pm& \stackrel{\bar s\bar c}{sc},\stackrel{\bar d\bar c}{dc} & \stackrel{\bar b\bar b}{bb},\stackrel{\bar d\bar d}{dd} & \eta_b, \eta_c, D^0, \bar {D^0}\\ 121.95 &92.274 & \stackrel{\bar u\bar u}{uu}& \mu, s_{rgb} , \nu_1, t_{rgb}& \pi^\pm, K^\pm& \stackrel{\bar s\bar u}{su}, \stackrel{\bar d\bar u}{du}& \stackrel{\bar s\bar s}{ss}, \stackrel{\bar s\bar d}{sd}& \eta_8, \pi^0, K^0, \bar K^0 \\ 0 & 0.0356 & \\ 8.75 & 5.32 & \\ \hline \end{array}$$

What one could look here is for mass sum rules of the kind expected in supersymmetry breaking, say
$$\sum_{bosons} M_i^2 = 2 \sum_{fermions} M_ i^2$$

I am unable to find any, perhaps some other can try. The best thing I see is for the six charged mesons, but using mass instead of its square, and and extra factor sqrt(2) too:

$$\sum_{bosons} M_i = 2 \sqrt 2 \sum_{fermions} M_ i$$

Where the mass levels of "fermions" are the three "before breaking" from the waterfall, and the masses of "bosons" are the experimental ones. A bit disappointing, but I name it just in case that such mass rule happened to be in the literature.

Code (Text):

(6274.9+5279.32+1968.28+1869.59+493.677+139.57061)/(2*(3640+1698+121.95))
1.4675351981

(6274.9+5279.32+1968.28+1869.59+493.677+139.57061)/(2*(4197.57589+1359.56428+92.274758))
1.4183183404

sqrt(2)
1.41421356237

Last edited: Jun 24, 2017
12. Jun 28, 2017

### arivero

Thinking about this. Do they have just the pion without parter, or does it happens that every meson or diquark does not have a partner for its lower energy state?

The absence of partner is a very general result of SUSY QM, coming from the witten index of the superpotential, but I wonder if it could be bypassed somehow, perhaps with imaginative use of dirac delta functions, different backgrounds, etc.

Last edited: Jun 29, 2017
13. Jul 2, 2017

### mitchell porter

I have not run across any fundamental barrier to the existence of superpartners for pions in supersymmetric field theory. It would appear to be just an example of the Goldstone fermion construction for a supersymmetric nonlinear sigma model (like Kugo-Yanagida), for the specific case of the supersymmetrization of chiral symmetry breaking. The paper in #222 may provide an explicit example of this. The main complication in constructing such models seems to be anomaly cancellation, which may require spectator fields.

On the other hand, Brodsky et al are employing, not supersymmetric field theory, but supersymmetric quantum mechanics. The archetype of supersymmetric quantum mechanics is an oscillator with one bosonic and one fermionic degree of freedom. It's nonrelativistic; supersymmetry as the square root of spatial translation comes about when you introduce relativity. Supersymmetric quantum mechanics can be obtained from a finite-volume limit of supersymmetric field theory - this is how Witten applies his index to field theories.

But I don't know how to obtain Brodsky et al's superconformal quantum-mechanical model of hadrons from a field theory. Their model only works because of the diquark-antiquark mapping that is specific to SU(3), and they don't worry about where that comes from. "Orientifold planar equivalence" does explain it in terms of a mapping from SQCD, to QCD with a quark in the antisymmetric two-index representation (thus, like a diquark), so maybe Brodsky et al can be obtained as a limit of an "orientifold field theory" (perhaps by way of a holographic interpretation of one of its stringy implementations).

14. Jul 2, 2017

### arivero

Well, but we know that we need a trick specific to SU(3) too, so any work searching under this lampost is welcome.

Of course if would be preferable if even SU(3) can be inferred. For instance, from compactification down from 8 or 9 dimensions, guessing that SU(3)xU(1) lives in extra CP2 x S1.

Recently I was thinking if it can be inferred from some need of consistency, even simply from contemplating the need of having all the scattering diagrams. I mean, consider the four pions scattering

I should be able to consider also the diagrams with quark lines going in reverse direction, and this is diquark-pion scattering, with a diquark in one channel and still one pion in the other (not sure which one is s and which t).

Could it be that this is actually posible only, if and only if, the colour group is SU(3)? Even the trick that hides this diagram into a Nucleon-Pion scattering, namely to add another quark line

seems a very SU(3)-ish trick. For lange N, we find ourselves adding N-1 parallel lines to build the barion, while here it still looks elegant.

EDIT: there is a small comment from Mandelstam about G-parity at the end of his short letter https://inspirehep.net/record/83802?ln=es telling that "We could also construct a model with $qq$ intermediate states where we do identify the two g-parities". This is, as opposite to the interpretation discussed in the paper, with only $q \bar q$ mesons and where "we cannot identify Neveu-Schwarz g-parity with physical g-parity".

Last edited: Jul 2, 2017
15. Jul 3, 2017

### arivero

Today, some history.

"QUARK OR BOOTSTRAP: TRIUMPH OR FRUSTRATION FOR HADRON PHYSICS? "

I have been reading this discourse, which Chew sent to the Physics Today in 1970; preprint is available here: https://pubarchive.lbl.gov/islandora/object/ir:144169/datastream/PDF/view

Most of it pivots about the different feeling that Chew students and collaborators have about having free parameters. Later this year, Veneziano (Phys Lett 24B, p59) opens an article referring confrontation ally to this one "One of the most common arguments [Phys Today 1970] against considering duality a genuine bootstrap scheme, is that..." And the same year, one of the students of Chew publishes the foundation articles of D=10 superstring theory, at the same time that, citing the previous two, claims to be not worried about the impossibility of fixing all the parameters; in NucPhysB31, p85, Schwarz and Neveu tell that "One possible attitude, closely akin to the bootstrap philosophy, is that of all the many dual model that might be constructed, only the right one is free of ghost and tachyons and gives a pomeron pole. Veneziano has further suggested that even the coupling constant can be determinable. However, this is an attitude we do not share".

So it seems that more than evolving from the bootstrap, string theory was born under the crossed fire between "fundamentalists" and "bootstrapers". This could explain why the wrong turn... under fire, it is more important to move anywhere than to know where to go. The first models try to have some quark content, but the failure to include strangeness drives the stringers to abandon this side too. At the end, they land in the undisputed land of quantum gravity.

Relating to the topic of this thread, this paragraph sounds encouraging, even if the answer of the superBootstrap is not the one that Chew is wishing here:

16. Jul 4, 2017

### arivero

Hmm, fast question: In the R-NS Dual Model, are the diquarks forbidden? If so, how?

(I mean, with the original interpretation where the Ramond sector are quarks, and the NS sector has a "quark-antiquark" sector and a "zero quarks" sector.

17. Jul 6, 2017

### arivero

Reviewing the thread I find this "joke", and while I can not find any relation to string nor group theory, it could we convenient to list the whole construction.

Point is, we consider the general case of r "isospin up" quarks and and s "isospin down" quarks, inserted inside a complete set of n generations. We can try arbitrary values of r and s and see how many scalars the system produces and so how

$$\begin{array}{l|c|r|r} & \text{formula} & r=2, s=3 & r = 16, s = 31 \\ \hline \text{down sector} & r s & 6 & 496 \\ \text{up sector: }&s (s +1 )/2 & 6 & 496 \\ \text{4/3 sector: }& r (r +1 )/ 2 & 3 & 136 \\ \text{muon sector: }&r s & 6 &496 \\ \text{neutral sector:} &(r^2 + s^2 - 1 ) / 2 & 6 & 608 \\ \text{of which, "extra neutrals" } & {(r^2 + s^2 - 1 ) / 2 - r s \\ = ((r - s) ^2 -1) / 2 }& 0& 112 \\ \text{so that 4/3 + extra neutrals:} & & 3 &248 \\ \hline \text{total quark sector} & (r + s) (r+s+1) / 2 & 15 & 1128 \\ \text{total lepton sector} & (r+s)^2 -1 & 24 & 2208 \\ \end{array}$$
The topic in this thread was that it is pretty natural to force the r=2 s=3 solution, e.g. asking for the four standard model charges to give the same number of bosons, or asking for zero neutrals and some other equality. And one wonders if there is some argument that makes logical the r=16 s=31 option, which could have some hope to be matched with superstring-originated groups.

Note that once it has been fixed that s = 2 r - 1 (by asking equal number of up and down bosons) then the formulae are
$$\begin{array}{l|c} & \text{formula} \\ \hline \text{down sector} & r (2 r -1) & \\ \text{up sector: }& r (2 r -1 ) \\ \text{4/3 sector: }& r (r +1 )/ 2 \\ \text{muon sector: }&r (2 r - 1) \\ \text{neutral sector:} &( 5 r^2 - 4 r ) / 2 \\ \text{of which, "extra neutrals" } & r (r - 2 ) / 2 \\ \text{so that 4/3 + extra neutrals:} & r ( 2 r -1) /2 \\ \end{array}$$

So that it seems that this condition also fixes that the sum of extra particles amounts to one half of the other sectors.

Note also that, being based in SU(5) flavour, the r=2 s=3 solution can be also seen as related to SO(10): the sum of quark, antiquark and leptons is 15 + 15 + 24 = 54, and indeed the 54 of SO(10) decomposes down to SU(5) irreps following this sum. On the other hand, the similar game in the big solution should involve SU(47) and SO(94), too big a game.

18. Jul 7, 2017

### mitchell porter

Here's a thought. Suppose we have six quark superfields with electromagnetic charges as in the SM, and a gluon superfield; and then suppose we make one of the up-type quark superfields very heavy. (I'm also going to ignore, for now, the photon superfield implied by the electromagnetic charges.)

What kind of objects can form at scales below the "top quark mass", in this scenario? We have five flavors of quark and squark, and we have gluons and gluinos. Let's suppose we can have gluon-strings and gluino-strings, terminated by quarks and squarks.

A quark-antiquark gluon-string is just an ordinary meson. A quark-antiquark gluino-string could be a lepton, as in the sBootstrap. And the other interesting twist is that a quark-squark gluon-string is reminiscent of a QCD baryon, if you think of a squark as like a diquark. Also, a squark-antisquark gluon-string is then analogous to a tetraquark; so it's like Brodsky.

We also have gluino-strings containing squarks - a new type of extra state. But what I find interesting, is that this scenario begins to incorporate the whole sBootstrap. Lepton-meson supersymmetry is there overtly, and quark-diquark supersymmetry, somewhat covertly.

19. Jul 10, 2017

### arivero

Yep, but one would need to find that a gluino string, because of some unknown, shows in low evergy as a point-particle, while a gluon string shows as an extended one. Hard to swallow, particularly because the strings have never presented a structure function similar to the experimental ones. Not the same partons, it seems :-(

I am thinking of a roadmap for the sBootstrap that could be palatable to stringers.

First, look at bosonic oriented strings and note that the SO(10) Chan Paton symmetry on it implements three generations of scalars in the tachion.
Separate mesons from diquarks by finding some oriented mesons inside this unoriented string. This could be problematic as usually the quotient goes in the reverse direction. But it could be doable.
Then argue that SO(10) is justified by a supersymmetric bootstrap: that light Dirac superpartners of these scalars must generate again the same sector. This for itself is already an argument to introduce fermions.
Now go down from D=26 to D=10 and try to keep this symmetry alive. Perhaps in the D-instanton, which has SO(10), or perhaps with some creative use of Marcus-Sagnotti fermion labels.
Now, our strings are still in some sense decolored, or SU(N-->infinity), and need to have chiral electroweak charge, instead of only electromagnetic. We should solve this when going down to D=4; the process of going from D=10 to D=9 would assign the broken electroweak components, and D=9 down to D=4 would paint the string with flying SU(3) colours plus B-L numbers.

EDIT: let me add the tables of the SO(10). The 54 down to $SU(5) \times U_1(1)$
$$54 = {15}(4) + \bar{15}(−4) + {24} (0)$$

Then each representation goes down to $SU(3) \times SU(2) \times U_2(1)$
$$\begin{eqnarray*} 15 =& (1, 3)(−6) + (3, 2)(−1) + (6, 1)(4) \\ 24 =& (1, 1)(0) + (1, 3)(0) + (3, 2)(5) + (\bar 3, 2)(−5) + (8, 1)(0) \end{eqnarray*}$$
And from the two hypercharges, we can produce a charge Q

$$\begin{array}{l|c |r|r|c} % a/b = 1/6 or = 2/3???? flav & N& Y_1 & Y_2& Q= \frac 1{30}Y_1 - \frac15 Y_2 \\ % Q= -\frac 2{15}Y_1 - \frac15 Y_2 \hline (6,1) & 6 & 4 & 4 & -2/3 \\ (3,2) & 6 & 4 & -1 & +1/3 \\ (1,3) & 3 & 4 & -6 & +4/3 \\ (\bar 6,1) & 6 &-4 & -4 & +2/3\\ (\bar 3,2) & 6 & -4 & 1 & -1/3\\ (1,\bar 3) & 3 & -4 & 6 & -4/3\\ (\bar 3,2)& 6 & 0 & -5 & +1 \\ (3,2) &6 &0 & 5 & -1 \\ (1,1) & &&& \\ (1,3)&12 &0& 0& 0 \\ (8,1)& &&& \\ \end{array}$$
On the other hand, it is tempting to try some hypercharge that puts away the chiral (1,3) squark

Last edited: Jul 10, 2017
20. Jul 13, 2017

### mitchell porter

There is no shortage of theoretical options to investigate. But I now prefer to think of quark-diquark supersymmetry as something which manifests only at the end of an open string, as in Brodsky. In #225 I mentioned that in Seiberg-Witten theory there are N=2 theories in which a single-particle state in one vacuum, can correspond to a multi-particle state in another vacuum. There is also the interesting "diquark monopole" of Vachaspati's dual standard model, which can decay into two "quark monopoles".

So what I would envisage, is a UV theory which is a perturbation of some self-dual supersymmetric theory - N=2 Nf=6 Nc=3 SQCD is still attractive as a candidate for that self-dual theory - which in the IR gives rise to the standard model. From the UV perspective, the IR fields of the standard model would be composite, as in a Seiberg duality, but there is some resemblance between the IR spectrum and the UV spectrum, because of the self-duality.

I would also still think in terms of getting both leptons and hadrons from a single IR theory of open strings, in which all strings are terminated by "quarks" (I'm not sure whether they would be IR quarks or UV quarks). Mesons and baryons are bosonic strings terminated by "quarks", leptons are fermionic strings terminated by "quarks".

Quark-diquark supersymmetry, as the part of the sBootstrap that most resembles a self-duality, would be an echo in the IR of that true self-duality in the UV, and would only pertain to the "quarks" that terminate the strings of the IR string theory. Lepton-meson supersymmetry, on the other hand, would be a supersymmetry of the whole string.

There are various challenges for such an approach, but I consider the main problem to be, getting to chiral fermions. The sBootstrap as currently formulated seems to apply to a non-chiral, SU(3) x U(1)em limit of the standard model, that would be expressed in terms of Dirac fermions with electric charge.

I thought further progress might require a careful review of all the phenomena and interactions of that non-chiral limit, and how they are explained by the true standard model in terms of Weyl fermions with weak hypercharge. Then one could take a non-chiral framework like that in #238, and try to elaborate it in an analogous way.

But it looks like you have just posted a concrete proposal for a hyperBootstrap. If it does make sense, it could immediately serve as the basis for a chiral N=1 field theory as in #222, which could then be studied with a view to IR behavior, formation of nonabelian strings, and so on - whether or not we also had a way to realize it in string theory.