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

[mitchell porter]

Massless QCD spontaneously breaks part of chiral symmetry (http://www.nikhef.nl/pub/theory/academiclectures/sm06_three.pdf). And in a standard model with no Higgs and massless fermions, the quark condensates do have the right quantum numbers to break electroweak symmetry a little - see Quigg and Shrock, II.A.1 and II.B.1. Here's an informal description of the resulting physics (also see this talk by Quigg).

 

[lpetrich]

From PDF page 20, the nonperturbative-QCD ground state has

<\bar Q_L \cdot Q_R> = <\bar u_L u_R + \bar d_L d_R + \cdots>

How would the quark fields "know" which ones to pair up with in the massless case? In the massive case, it's easy: the mass eigenstates.

 

[mitchell porter]

It seems (see page 20 of Wilczek's latest) that the degenerate ground states of massless QCD are indexed by unitary matrices (the matrix elements being VEVs like <\bar q_{jL} q_{kR}>, j and k flavor indices), and that the quark fields would be defined as the operator basis which diagonalizes the matrix.

 

[mitchell porter]

Alejandro's revisit to Koide 1981 (publication, preprint) in the other thread prompts me to outline yet another what-if scenario.

In Koide 1981 there are three generations of preons. In each generation, there is a subquark doublet with color charge, a subquark doublet with subcolor charge (subcolor is an extra SU(3) interaction), and a subquark "h", also with subcolor charge. (The left-handed part of the doublets is a weak doublet, the right-handed part is two weak singlets.)

One generation of SM leptons consists of the subcolor-charged doublet coupled to an subcolor-antisymmetric combination of two "h" subquarks, producing a lepton which is a subcolor singlet. One generation of SM quarks consists of the color-charged doublet coupled to a subcolor-singlet meson "h-hbar", producing particles which are subcolor singlets but color triplets. Koide admits the model doesn't explain why the doublet and the meson are bound together.

Curiously, this is the reverse of the sbootstrap, in the following sense. In Rivero 2005, quarks are associated with diquarks and leptons with mesons. In Koide 1981, leptons are associated with di-preons and quarks with pre-mesons.

Can we build the sbootstrap out of subcolor, but with "diquarks" in quarks and "mesons" in leptons? Here one faces the usual stumbling block that in the sbootstrap, we seem to be building quarks out of themselves. So I propose to proceed as follows. We are to think of the SM as dual to a model containing six quarks only, which we shall label t', b', c', s', u', d'. We are to think of t' as massive and the other five as massless.

Finally, we suppose that these dual quarks all have subcolor charge as well as color charge, and that there is a further dual-quark doublet n1, n2 ("n" for neutral), with subcolor charge, but no color charge or electromagnetic charge.

Now we can proceed in imitation of Koide, but in reverse. SM leptons combine n1, n2 with ordinary-color dual-mesons, producing particles that are color singlets and subcolor singlets. SM quarks combine n1, n2 with color-antisymmetric dual-diquarks in the anti-triplet representation, producing particles that are also subcolor singlets, but which are color anti-triplets, just like the original form of "hadronic supersymmetry". Or rather, SM quarks are "partially composite"; they are mixtures of the original dual-quarks with these quark-like subcolor-baryons.

So we have a duality between a model with six "dual quarks", one heavy and five massless, and no leptons; and a model with six quarks and six leptons of various masses. If we think of these as superfields, one might even suppose that this is a duality between two models of mass generation discussed recently in the thread, the "radiative" model in which only the top has a tree-level mass and all other SM fermions get their masses through loop effects, and the "circulant" model in which there are 3 or 6 higgses (the emergent sleptons) producing circulant mass matrices. (And perhaps the n-quarks are subcolor gauginos, and perhaps there will be a stringy model of the "subcolor baryons".)

 

[arivero]

Mitchell, have you noticed in the bibliography on composite Higgs equations such as

y_{u,d}\sim \lambda_{u,d}\lambda_q \sqrt {N/4\pi}

? I guess that the lambdas are a kind of square roots of mass.

 

[arivero]

How does the condensation "technicolor" work for the electroweak group? If I understand it, we need to give mass to three vector particles and produce three goldstone bosons. Thus the real comparision is not to flavour SU(3), that produces an octect of goldstones, but to flavour SU(2), and then the triplet of pions should be a triplet of higgses H+, H-, H0, and another three degrees of freedom are eaten to give mass to the rho.

I think that the role of the "u,c terminated strings" in the sBootstrap is a even more retorted version of this, involving pairs of particles instead of particle/antiparticle, and some B-L juggling to adjust the charges. But it is amazing that then the top condensate is not involved ever in the Higgs mechanism. Does the sBootstrap have some hidden role for the top condensate, or we are really so strict about not allowing it to bind to any object in any situation?

 

[arivero]

"u,c terminated strings" ... and some B-L juggling to adjust the charges.

The point is that Q = T3 + (B-L)/2.

So if we uncouple B-L, a quark only offers an electric charge from T3, this is +1/2 for the up quark, -1/2 for the down. The T3 can be R or L.

So you see, uu, uc and cc could produce three Q=+1 bosons very nicely, and the antiparticles the corresponding Q=-1 But the problem is that we need to have two Q=0 bosons in the pack.

The most obvious way is to have one of them, say c, with a T3=-1/2. But then it should have B-L equal to 7/3 to compensate, for instance keeping B=1/3 but L=-2 instead of 0. Either that, or some other mechanism I am missing yet.

Had we such mechanism, we had a prediction of a higgs sector from condensates with a neutral H0 and two charged H+ H-

 

[mitchell porter]

I think the idea is unlikely. However, I will point out Mohapatra et al on an up-type sextet diquark Higgs. Your diquark Higgs might also need a B-L spurion to work.

There was a paper proposing that the 125 GeV boson is in fact a mixture of toponium and bottomonium. (Interestingly, the other mixed eigenstate has a mass close to 325 GeV, where there were anomalies last year.) One could look for a connection with topcolor, topcolor-assisted technicolor, and/or pion-Higgs models.

 

[arivero]

Mohapatra et al

Somehow the academics now how to get their stuff published. Not that they get more impact that us, although.

I am pretty sure that it is possible to do the first part, to get rid of colour and B-L on the argument that they are pure vector forces. The problem remains of genning a neutral boson out of it.

 

[arivero]

I think the idea is unlikely. However, I will point out Mohapatra et al on an up-type sextet diquark Higgs.

It is interesting that in this kind of models the uu diquarks have different mass scale than the dd. I guess that it is related to the different scales of electrons and neutrinos in the lepton side of the model.

 

[mitchell porter]

There is no fundamental dd diquark in that model. The "diquark" here is a scalar with a diquark coupling, not a QCD diquark.

If you follow the references back, the 2007 paper cites a 1998 paper which cites a 1980 paper which talks about Higgses made of bound states of fermions. It doesn't call them diquark Higgses. Actually I can't parse the figure in that paper; it seems the Δ_R,44 is the scalar with a VEV, then it has an interaction with three other scalars, and then they interact with quarks and induce a ΔB=2 transition. So the "diquarkness" might be hiding in that diagram somewhere. But that's the best I can do, in the search for a diquark Higgs which is a genuine QCD diquark.

Another consideration is that QCD diquarks are not gauge invariant. A diquark condensate breaks the gauge symmetry, it's involved with phenomena like color-flavor locking and color superconductivity. I can imagine that such exotic phenomena play a role in the appearance of QCD scales in the Koide triplets, e.g. maybe they help to hide a second confining SU(3) interaction, as in the amended version of Koide 1981 that I proposed. But I do think a chiral condensate (qqbar, not qq) is a more plausible way to get EWSB.

In sbootstrap language, diquark -> squark and meson -> slepton. There's a small literature on sneutrino Higgses, but I can't see anything at all about a "squark Higgs". (There is some stuff out there, about squark condensates and CFL in holographic QCD.) But this difference of opinion shouldn't be too much of a problem, the big picture probably involves both chiral condensates and diquark condensates and we'll have to understand both.

 

[lpetrich]

So this is about some particle in a 6 (20) representation of QCD SU(3)?

That is a symmetric square of the fundamental representation, 3 (10); its antisymmetric square is 3* (01).

Since hadron states are all color singlets (colorless), a 6 needs to combine with a 6* (02), like its antiparticle, or a 3 (10) and an 8 (11), like a quark and a gluon:

6(20) * 6*(02) = 27(22) + 8(11) + 1(00)
6(20) * 3(10) = 10(30) + 8(11)
8(11) * 8(11) = 10(30) + 10*(03) + 27(22) + 8(11) + 8(11) + 1(00)

To combine with the quarks and yield integer electric charges, it must have antiquark-like electroweak quantum numbers, with
(weak hypercharge) = (weak isospin) + 1/3 + (integer)

 

[lpetrich]

Let's see about Georgi-Glashow SU(5).

24(1001) = (8,1,0) + (1,3,0) + (1,1,0) + (3,2,-6/5) + (3*,2,6/5)
5(1000) = (3,1,-1/3) + (1,2,1/2)
10(0100) = (3,2,1/6) + (3*,1,-2/3) + (1,1,1)
10*(0010) = (3*,2,-1/6) + (3,1,2/3) + (1,1,-1)
5*(0001) = (3*,1,1/3) + (1,2,-1/2)

To get 6 and 6* QCD states, one can use
15(2000) = (6,1,-2/3) + (3,2,1/6) + (1,3,1)
15*(0002) = (6*,1,2/3) + (3*,2,-1/6) + (1,3,-1)
and similar decompositions for 40(1100), 50(0200), 45(1010), etc.

GG automatically makes every color singlet have integer electric charge.

One can go further, in the likes of SO(10) and E6, but one gets even more extra particles.

 

[arivero]

So this is about some particle in a 6 (20) representation of QCD SU(3)?

Yes and no. The particles in these articles come from usual GUT theory. The ones in the sBootstrap comes from a 15 of SU(5) flavour, still to be seen if it is relevant to see them also as SU(3) colour antitriplets.

 

[arivero]

Funny. The guy in the left corner in the Strings 2008 closing lecture (the one with the blue shirt) seems to be busy thinking about orientability of the worldsheet and diverse wrappings. I had not noticed it before.

http://cdsweb.cern.ch/record/1121966

 

[mitchell porter]

"A Higgslike Dilaton". There have been many such Higgs-vs-dilaton papers. This one examines the situation where the theory is supersymmetric and the SM fermions are partly composite (i.e. are mixtures of elementary and composite fields with the same quantum numbers), a scenario discussed several times in this thread.

 

[arivero]

"A Higgslike Dilaton". There have been many such Higgs-vs-dilaton papers. This one examines the situation where the theory is supersymmetric and the SM fermions are partly composite (i.e. are mixtures of elementary and composite fields with the same quantum numbers), a scenario discussed several times in this thread.

Big guys in the paper. And then it shows how half-baked our speculations are, if you consider the difficulties they have to formulate a decently realistic model. But it is encouraging that they consider partial compositeness as a part of the play.

 

[mitchell porter]

Ramond et al had a paper, "On Mixing Supersymmetry and Family Symmetry Breakings", in which "extra family partners of the Higgs particles act as messengers for both supersymmetry and family symmetry breakings". It's mildly interesting to contemplate how the waterfall and/or sbootstrap might be realized in a framework like this, because this is a serious, calculable field-theoretic model.

The first thing to note is that it talks about supersymmetry breaking, and also how it is accomplished. There are several new scalar fields in the Higgs sector, and one of them is postulated to be coupled to a hidden sector where supersymmetry is broken. This messenger field then acquires vevs which break susy (and family symmetry), and the breaking is then transmitted to the rest of the visible sector (MSSM plus new scalars). This transmission of susy-breaking from a whole new sector where the breaking originates is completely standard; it's "single-sector supersymmetry breaking" which is the unusual alternative to mediated susy-breaking.

By contrast, the papers which introduce the sbootstrap hardly talk about susy-breaking. In fact, among the inspirations for the sbootstrap are coincidences like the similarity of the muon mass and the pion mass. Another question hanging over the sbootstrap is how much of conventional thinking about supersymmetry it wishes to take on. In the conventional MSSM, the muon is the superpartner of certain sleptons, and the pion is still a QCD composite and has no relation to those sleptons at all. In the sbootstrap, one supposes that the muon is the superpartner of something decidedly pion-like (and in fact all the leptons are "superpartners" of pion-like quark-antiquark combinations). So it seems that something like the MSSM is supposed to be emergent from something like SQCD. (An alternative approach might be to say that the MSSM has its normal interpretation - sleptons and pions are fundamentally different - but that it has a peculiar hidden N=2 supersymmetry, with the sbootstrap correspondence being the emergent second supersymmetry.)

Second, let's consider the role that family symmetry plays in the sbootstrap and the Koide waterfall, and then in Ramond et al. Alejandro describes the sbootstrap as featuring an SU(5) global flavor symmetry, and family symmetries have also featured in many attempts to explain the Koide formula.

The family symmetry considered in Ramond et al is discrete and very simple, the permutation group S3, and so is the model; it's not even a three-generation model, there are only two "families". This isn't yet a serious phenomenological model, it's a toy model of how symmetry-breaking messenger particles (here, some of the new scalars) could carry flavor and yet not cause detectable flavor-changing neutral currents. The physics that results depends greatly on the specific vacuum and on renormalization-group effects. These technicalities would be relevant for any serious attempt to embed sbootstrap and waterfall in such a model, and at first glance they don't look very friendly for the generation of Koide-type relationships, but a real assessment on that score awaits a deeper analysis, especially of the "focusing mechanism" which, for certain vacuum alignments, produces phenomenologically convenient cancellations.

So overall this is an interesting class of model to examine, for potential implementations of sbootstrap and waterfall, because by design it addresses the issue (neglected by us) of how the symmetries get broken.

 

[mitchell porter]

Two unorthodox top/Higgs papers today. John Moffat continues his series suggesting that LHC's new boson is not a Higgs, but rather a pseudoscalar meson, a mixture of b \bar b and t \bar t. And Christopher Hill, inventor of "topcolor", observes that the "top-Higgs system" has a susy-like dilatation symmetry, which he uses to explain a web of relations between the top yukawa, the Higgs mass, and the Higgs VEV.

These papers should be considered in conjunction with Bruno Machet's attempt to build Higgs doublets out of quark bilinear condensates (#149) and with "A Higgslike Dilaton" (#166). With respect to the sbootstrap, Moffat and Machet remind us that the "mesons" and "diquarks" of the correspondence might be condensates (but what is the superpartner of a condensate?), and Hill reminds us that an unorthodox "supersymmetry" may be at work. Also, these papers remind us that there remain many relatively elementary constructions that have never been considered.

One more thought. In Hill's paper, he argues that alongside top yukawa being close to 1, LHC has revealed that the Higgs quartic coupling is close to 1/4. Numerologically I am reminded of Yukinari Sumino's scheme for cancelling QED corrections to the Koide relation, which requires that the coupling of the new family gauge bosons is approximately 1/4 of the QED coupling. Sumino had no explanation for this relation; could Hill's new symmetry do the job?

 

[arivero]

Two unorthodox top/Higgs papers today.

Well, as a minimum, it shows that Perimeter and Fermilab have an allowance for exotic thoughts

 

[arivero]

The peculiar arrangement of SU(4), or U(1)xSU(3) multiplets noticed in the Koide thread

https://www.physicsforums.com/showthread.php?t=551549&page=6

could be related to the problems to put the higgs scalar under the same symmetries that the other scalars in the sboostrap.

Remember that we had to our disposal three scalars from the 15 and other three from the 15 irreps of SU(5). In our quark mnemonics, it is uu, uc, cc, uu, uc, cc (using the underscore to mean antiparticle). For such thing to be able to produce integer uncoloured charges, we need the mass/higgs mechanism to be blind to colour and blind to B-L, so that all the electric charge of these objects come from the electroweak isospin. Thus here is the first connection to the other thread: the multiplets of equal mass are for the charges for which the sBootstrap Higgs, if it is there, needs to be blind.

The second connection is even foggier: in the other thread, either the strange quark or the muon seem to need an opposite quantum number in order to fit in a SU(4) multiplet. Here it is either the up quark or the charm quark which seem to need some opposite value to sum zero in the uc combination.

 

[mitchell porter]

Two recent papers, by authors already mentioned in this thread, which derive a Higgs sector in a sbootstrap-friendly way:

Bruno Machet continues his series "Unlocking the Standard Model" (see #149), in which the idea seems to be that the Higgs will come from pion-like vevs. As discussed e.g. in #151, in a Higgsless SM, the W and Z will still acquire masses from pion vevs, but at the wrong energy scale. Machet nonetheless wants a version of this to work. In this, his third paper in the series, he considers two generations of quarks, and claims to get the Cabibbo angle from his Higgs-like condensates. Presumably future work will aim to get the whole CKM matrix from the quark bilinears of a three-generation model. Of the multitude of scalar and pseudoscalar mesons that appear, he states (page 4) that some of the scalars will be the Higgs, and the rest should correspond to the observed mesons.

Kitano and Nakai's "Emergent Higgs from extra dimensions" aims to get the Higgs (and the masses of the Higgs and the top) from a deconstructed compactification of the d=6 (2,0) theory to four dimensions. This paper is certainly replete with connections to interesting topics. The (2,0) theory is the worldvolume theory of the M5-brane, so it's central to current advances in theoretical QFT. Their deconstructed version (deconstruction here means that the extra dimensions are approximated by a lattice, so e.g. a circle becomes a ring of sites with a copy of the d=4 SM fields at each site, coupled via the links in the ring, as in a quiver theory) is said to resemble topcolor (see page 3). There's much more I could talk about and I may have to return to this paper. But for now I'll remark on the possibility that perhaps something like Machet's model, which naively shouldn't work, could be produced by a Kitano-Nakai scenario, in which new strong couplings occur at high energy. "As in the Nambu–Jona-Lasinio model for the chiral symmetry breaking, whether or not a condensation forms depends crucially on how the theory is cut-off, and thus discussion requires a UV completion of the theory."

 

[arivero]

The peculiar arrangement of SU(4), or U(1)xSU(3) multiplets noticed in the Koide thread
https://www.physicsforums.com/showthread.php?t=551549&page=6

Back to this, let's approach diquark masses with the mass of the heaviest quark, or the QCD mass if it is heavier than the quarks themselves. Then we can add mesons and diquarks to the "SU(4) arrangement".

\begin{array}{lllll}<br /> ?, t_{rgb}&amp; &amp; &amp; &amp; \\<br /> ?, b_{rgb}&amp; B^+,B_c^+ &amp; bu, bc&amp; bb, bs, bd &amp; \\<br /> \tau, c_{rgb} &amp; D^+, D_s^+&amp; sc,dc \\<br /> \mu, s_{rgb} &amp; \pi^+, K^+&amp; su, du&amp; ss, sd, dd \\<br /> ?, d_{rgb} \\ <br /> e, u_{rgb}\end{array}

It is tempting to think that in this "midly broken susy", the two lower mass levels are actually massless, so that SUSY does not need to kept the pairing at the same mass; it could be that the partners of d are the charmed diquarks, while the partners of up have been lost in the same mixing that breaks t and c partners.

Adding neutrinos and the missed diquarks, the table is a bit more complex. With some small abuse of notation, we could write the "after mild breaking" sBootstrap as

\begin{array}{lllllll}<br /> &amp;\nu_?, t_{rgb}&amp; &amp; &amp; &amp; \\<br /> &amp;\nu_?, b_{rgb}&amp; B^+,B_c^+ &amp; bu, bc&amp; bb, bs, bd &amp; \eta_b, \stackrel{b\bar s,b\bar d}{\bar bs,\bar bd} \\<br /> \stackrel{\bar c\bar c}{cc},\stackrel{\bar c\bar u}{cu}&amp;\tau, c_{rgb} &amp; D^+, D_s^+&amp; sc,dc &amp; &amp; \eta_c, \stackrel{c\bar u}{\bar cu}\\<br /> \stackrel{\bar u\bar u}{uu}&amp;\mu, s_{rgb} &amp; \pi^+, K^+&amp; su, du&amp; ss, sd, dd &amp; K^0,\pi^0, \stackrel{s\bar d}{\bar sd}\\<br /> &amp;\nu_?, d_{rgb} \\ <br /> &amp;e, u_{rgb}\end{array}

It is sort of symmetric, in a pleasant way. Wish I knew what to do about it.

 

[mitchell porter]

We can adapt an earlier idea for the sbootstrap to Pati-Salam. The earlier idea is that there is a fundamental QCD-like theory with six flavors of quark, five light and one heavy; the five light quarks form fermionic composites, "diquarkinos" and "mesinos"; and the mesinos are the leptons, while the diquarkinos mix with the fundamental quarks to give us the phenomenological quarks.

For Pati-Salam sbootstrap, the prescription is almost the same, except that the leptons already exist as the "nth color" in the fundamental QCD-like theory, so in this version the mesinos are mixing with preexisting degrees of freedom, just like the diquarkinos.

It's probably best to think of the fundamental theory as having N=1 supersymmetry (at least), and to think of these composites as superfields.

 

[arivero]

http://higgs.ph.ed.ac.uk/sites/default/files/Higgs_RR.pdf

Rattazzi is near to discover the sBootstrap if he continues this kind of enquiries.

 

[mitchell porter]

On the Koide thread we have started to discuss textures and symmetries that could produce the waterfall pattern, and it's beginning to sound like orthodox model-building. But it's still not clear to me how to naturally descend from the sbootstrap to the waterfall. Supersymmetric theories are more complicated, including their methods of mass generation, and the "super-paradigm" which in my opinion most resembles the sbootstrap - Seiberg duality - doesn't offer obvious concrete guidance.

However, I have a few thoughts arising from one of the non-susy paradigms for modeling the masses. As described e.g. on page 2 here, one may imagine that SM yukawas arise from a democratic matrix plus a correction. The democratic matrix has eigenvalues (M,0,0), and the correction can make the smaller eigenvalues nonzero.

So consider an approach to the sbootstrap in which we begin with six flavors of chiral superfield, and in which some fundamental, democratic mechanism of mass generation produces a single heavy flavor. Now suppose that the five light flavors form meson superfields which mix with the fundamental superfields, as previously posited. It seems that we then have a mass matrix which starts with SU(6) symmetry and then has a correction with SU(5) symmetry; something which is ripe for further symmetry-breaking, perhaps down to a waterfall pattern.

There are still conceptual problems. The democratic matrix usually appears as a Yukawa matrix, but one doesn't usually think of the Higgs as fundamental in the sbootstrap. Also, the usual "five-flavor" logic of the sbootstrap is motivated by the fact that the top decays before it can hadronize; but that decay is mediated by the weak interaction, which doesn't yet play a role in the scenario above. There's also the problem that the combinatorics of the sbootstrap employs the electric charges of the quarks, but if we impose those from the beginning, then we can't have the exact SU(5) or SU(6) flavor symmetry. So there may need to be some conceptual tail-chasing before a logically coherent ordering and unfolding of the ingredients is found.

On the other hand, I wonder if some version of the cascades discussed earlier in this thread (page 9, #132 forwards) can produce an iterated breakdown of symmetry in the mass matrix. We could start with one heavy quark and five light, then the diquarkinos and mesinos induce corrections to the mass matrix, which in turn affect the masses of the diquarkinos and mesinos, breaking the symmetry further.

Also of interest: "Strongly Coupled Supersymmetry as the Possible Origin of Flavor".

 

[arivero]

I have put around an example about how the supermultiplets could be, before the susy breaking. Surely it is not the right mix, but it could be a reference to try to build a pure susy model. http://vixra.org/abs/1302.0006

<br /> \begin{array}{||l|l|llll||} <br /> \hline<br /> \stackrel{\bar c\bar c}{cc}&amp;<br /> \nu_2, b_{rgb}, e, u_{rgb}&amp; <br /> B^\pm,B_c^\pm &amp; <br /> \stackrel{\bar b\bar u}{bu}, \stackrel{\bar b\bar c}{bc}<br /> &amp; \stackrel{\bar b \bar s}{bs}, \stackrel{\bar b\bar s}{bd} &amp; <br /> B^0, B^0_c, \bar B^0, \bar B^0_c \\ <br /> \stackrel{\bar c\bar u}{cu}&amp;<br /> \tau, c_{rgb} , \nu_3, d_{rgb}&amp;<br /> D^\pm, D_s^\pm&amp;<br /> \stackrel{\bar s\bar c}{sc},\stackrel{\bar d\bar c}{dc} &amp; <br /> \stackrel{\bar b\bar b}{bb},\stackrel{\bar d\bar d}{dd} &amp;<br /> \eta_b, \eta_c, D^0, \bar {D^0}\\ <br /> \stackrel{\bar u\bar u}{uu}&amp;<br /> \mu, s_{rgb} , \nu_1, t_{rgb}&amp;<br /> \pi^\pm, K^\pm&amp; <br /> \stackrel{\bar s\bar u}{su}, \stackrel{\bar d\bar u}{du}&amp;<br /> \stackrel{\bar s\bar s}{ss}, \stackrel{\bar s\bar d}{sd}&amp;<br /> \eta_8, \pi^0, K^0, \bar K^0 \\<br /> \hline<br /> \end{array}<br />

 

[mitchell porter]

A major conceptual problem for the sbootstrap has been, how to get elementary and composite fields in the same superfield. But I notice that the string concepts of "flavor branes" and "color branes" can bring them closer. The flavor branes would be labeled dusc... and the color branes rgb..., and a single quark is a string between a flavor brane and a color brane (e.g. a red up quark is a string between up flavor brane and red color brane); and a meson is a string between two flavor branes. And if we employ Pati-Salam, then all the leptons also have a color, the "fourth color".

According to the sbootstrap, a lepton is the fermionic superpartner of some meson or quark-antiquark condensate. The immediate problem for achieving this within the framework above is that it seems to involve pairing up different types of strings. Usually, you suppose that the flavor branes form one stack, the color branes form a different stack, the two stacks lie at different angles in the extra dimensions, and there are three types of string: flavor-flavor, color-color, and flavor-color. As usual, each stack will have a corresponding symmetry (e.g. SU(N) for some N), the flavor-flavor strings will be singlets under the color group, the color-color strings (the bosonic states of which are the gluons) are singlets under the flavor group, and the flavor-color strings transform under both groups.

Also, the flavor-color strings are found most naturally in the vicinity of the intersection between the flavor stack and the color stack, because that is where the distance is shortest and thus the tension is smallest. But flavor-flavor and color-color strings can be found anywhere within their respective stacks, because the branes are parallel and so the inter-brane distance is the same everywhere. To my mind this poses a major barrier to the idea of placing a flavor-color string and a flavor-flavor string in the same multiplet.

What if, instead of using intersecting brane stacks, we just have one big stack, and then move the branes apart into two groups, while keeping them parallel? This is already a standard method of breaking a symmetry group - the gauge bosons corresponding to strings between the two parts of the stack are the ones that are heavy, because they are longer. Now we would have that G_flavor x G_color is a subgroup of G_big, the symmetry group of the original, unseparated brane-stack. Then we would suppose that the branes of the big stack are separated from each other in the extra dimensions (while remaining parallel) in such a way as to produce the desired mass spectrum - with the flavor branes clustered together in one group, the color branes in another, and the distances within and between the groups tuned appropriately.

 

[mitchell porter]

I'll sketch how something like this could work. We'll use nine D3-branes in a space of three large dimensions, and six small and compact dimensions. Geometrically it can be just like Kaluza-Klein, except that each local copy of the KK manifold has nine special points scattered throughout it, the places where the nine D3-branes pass through that copy of the KK space.

Basically, we would think of three of the points as being close together, and the other six scattered around them in six-dimensional space. The three branes that are close together (in fact, on top of each other) are the color branes. Because they are on top of each other, the SU(3)_color gauge symmetry is unbroken. But the other six branes are scattered around and the SU(6)_flavor gauge symmetry is completely broken.

The quark superfields are strings connecting the 3 coincident points with any of the 6 scattered points, and the meson superfields are strings connected the 6 scattered points with each other. And to get them into the same supermultiplets, you restore the symmetry by moving all 9 points so they are on top of each other.

So far I've said nothing about the weak interaction, and in fact I think it will require a doubling of the branes - or of the flavor branes at least. For each flavor there will be two branes, a "left brane" and a "right brane", for the two chiral components. Once again, this is a quite standard idea.

Hypercharge is no problem, it's just a particular U(1) subgroup. And I suppose we can hope that the desired arrangement of branes is produced dynamically, e.g. by relaxation from cosmological initial conditions.

It's surely too much to hope for, that some version of this would actually work. But I think it's remarkable that mathematically, this is genuine orthodox string theory. You could define a particular geometry for the Type IIB string (which is the one that has D3-branes) and calculate its spectrum.

edit: Wait, I forgot we were getting leptons from a fourth color. So there are four color branes, four "color points" in the KK space, but one of them is displaced a little from the others - the breaking of SU(4)_color to SU(3)_color. A single quark is a string connecting a flavor brane to an rgb color brane, and a lepton is a string connecting a flavor brane to the fourth color brane.

 

[mitchell porter]

We have a number of threads right now on getting the Higgs mass from Planck-scale boundary conditions. The common idea is that there is no new physics between the weak scale and the Planck scale. The best-known version is that of Shaposhnikov and Wetterich (SW), who managed to land very close to the observed mass by postulating that the "neutrino minimal standard model + gravity" is "asymptotically safe". However, I think the most elegant proposal is the "conformal standard model" of Meissner and Nicolai, who observe that the classical theory is conformally invariant except for the quartic Higgs term, and who propose therefore that the fundamental theory has conformal symmetry and that this quartic term is generated by the conformal anomaly.

I note that in the world of high theory now, the really interesting symmetry is superconformal symmetry, the combination of supersymmetry and conformal symmetry. And since the sBootstrap, like the conformal standard model, is an exercise in theoretical minimalism, I have to wonder if there could be a "superconformal standard model" combining both?

Supersymmetry is normally regarded as wildly incompatible with the minimalist idea of "no new physics between weak scale and Planck scale". We already know that we need physics beyond the original standard model with massless neutrinos; the "neutrino minimal standard model" manages to obtain all this below the weak scale, though at the price of unnatural finetuning (dark matter comes from right-handed neutrinos with keV Majorana mass, left-handed neutrino masses from very small yukawas). One might suppose that including supersymmetry would be even harder, or just impossible.

One approach would be supersplit supersymmetry: all the superpartners have Planck-scale masses. But what about the sBootstrap alternative: supersymmetry is there, but it's only very weakly broken? In a sense that's the longrunning theme of this thread - the quest for ways to embed the sBootstrap pattern within a genuinely supersymmetric theory.

The gauginos are the main technical problem that I see. One possibility is that we can just do without them by using Sagnotti's type 0 string theory, which is nonsupersymmetric but arises from the superstring, and which can apparently inherit a degeneracy of boson-fermion masses. Armoni and Patella use type 0 open strings to construct a form of "hadronic supersymmetry" (pairing mesons and baryons) - see page 8 for their general remarks on the type 0 theory. Meanwhile, Elias Kiritsis has sought to obtain a holographic dual for (nonsusy) QCD using type 0 strings. We have discussed the mesinos from holographic QCD several times; perhaps a type-0 version of the brane-stack constructions I discussed here a few weeks ago, could provide a "non-susy sBootstrap" in which we have mesinos but not gauginos.

So perhaps we might want a type-0 brane stack which classically has conformal symmetry, but in which the Fermi scale is anomalously generated (as in the conformal standard model). Meanwhile (bringing in ideas from the Koide thread), there's also a discrete S4 symmetry producing a Koide waterfall, with the top yukawa equal to 1 and the up yukawa equal to 0... The waterfall produces the quark mass ratios, the SW-like mechanism produces the Fermi scale. The leptons are fermionic open strings between the flavor branes in the brane stack (mesinos)... It's all still a delirium, but perhaps we're getting there.