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

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.

 

32 pages on how Thomson might have discovered supersymmetry

 

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).

[tex]
\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}
[/tex]

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

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:

[tex]\sum_{bosons} M_i = 2 \sqrt 2 \sum_{fermions} M_ i [/tex]

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
 

 

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.

 

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 [itex]qq[/itex] intermediate states where we do identify the two g-parities". This is, as opposite to the interpretation discussed in the paper, with only [itex]q \bar q[/itex] mesons and where "we cannot identify Neveu-Schwarz g-parity with physical g-parity".

 

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:

 

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.

 

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

[tex]
\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}
[/tex]
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
[tex]
\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}
[/tex]

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.

 

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 [itex]SU(5) \times U_1(1)[/itex]
[tex]
54 = {15}(4) + \bar{15}(−4) + {24} (0)
[/tex]

Then each representation goes down to [itex]SU(3) \times SU(2) \times U_2(1)[/itex]
[tex]
\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*}
[/tex]
And from the two hypercharges, we can produce a charge Q

[tex]
\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}
[/tex]
On the other hand, it is tempting to try some hypercharge that puts away the chiral (1,3) squark