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

arivero

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

http://www.physicsforums.com/showthr...=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

Back to this, lets aproach 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".

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

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

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

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/defau...s/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

[tex]
\begin{array}{||l|l|llll||}
\hline
\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 \\
\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}\\
\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 \\
\hline
\end{array}
[/tex]

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.

arivero

As for the relationship between the above folding and the S4 generalisation of Koide, I find that they are two solutions of the eight S4 simultaneus equations that seem relevant:

[tex]
\begin{array}{|ll|}
\hline
3.64098 & 0 \\
1.69854 & 1.69854 \\
0.12195 & 0.12195 \\
\hline
\end{array}
\dots
\begin{array}{|ll|}
\hline
b & u \\
d & c \\
s & t \\
\hline
\end{array}
\dots
\begin{array}{|ll|}
\hline
3.640 & 3.640 \\
1.698 & 1.698 \\
0.1219 & 174.1 \\
\hline
\end{array}
[/tex]

The one on the left appears when looking for zero'ed solutions; the one on the right appears in the resolvent of the system when looking for zero-less solutions; so both of them are singled-out very specifically even if, being doubly degenerated, they are hidden under the carpet of a continuous spectrum of solutions.

To be more specific: a S4-Koide system on the above "folded" quark pairings should be a set of eight simultaneous Koide equations, for all the possible combinations: bds, bdt, bcs, bct, uds, udt, ucs, uct. A double degenerated solution of such S4-Koide system lives naturally inside a continuum: the equation K(M1,M2,x)=0, with M1 and M2 being the degenerated masses, has multiple solutions for x, and any two of them can be used to build the non-degenerated pair of the folding.

The solution in the left is one of the possible solutions having at least a zero; up to an scale factor, there are only four of them. I have scaled it to match with the solution in the right.

The solution in the right is one of the solutions obtained by using the method of polynomial resolvents to solve the system of eight equations (actually, we fix a mass and then solve the four equations containing such fixed mass). It is scaled so that its higher mass coincides with the top mass.

For details on the calculation of the solutions, please refer to the thread on Koide.

mitchell porter

Some recent thoughts:

As with mainstream supersymmetry, I see the sbootstrap's situation as still being one where there is such a multitude of possibilities that it is hard even to systematically enumerate them. The difference is that a mainstream susy model consists of a definite equation and a resulting parameter space that then gets squeezed by experiment, whereas a sbootstrap "possibility" consists of a list of numerical or structural patterns in known physics which are posited to have a cause, and then an "idea for a model" that could cause them. It may be that some part of sbootstrap lore is eventually realized within a genuinely well-defined model that will then make predictions for MSSM objects like gluinos, or it may be that it will be a "minimalist" model that is more like SM than MSSM. (As for the Koide waterfall, that is such a tight structure, it seems that any rigorous model that can reproduce it is going to be sharply predictive - but there may still be several, or even many, such models.)

Today I want to report just another "idea for a model". It's really just a wacky "what if"; I don't know that such a model exists mathematically; but I'd never even look for it if I didn't have the schematic idea. The idea is just that there might be a brane model in which the top yukawa is close to 1 both in the far UV and in the far IR, and that this is due to a stringy "UV/IR connection".

The reason to think about this is as follows. The discussion of whether the Higgs mass might be in a narrow metastable zone, has yielded the perspective that it might be worth considering the top yukawa and the Higgs quartic coupling at the same time. The latter goes to 0 in the UV, the latter goes very close to 1 in the IR.

But Rodejohann and Zhang have observed that with massive neutrinos, the top yukawa can approach 1 at high energies as well (see pages 14 and 15; the minimum is roughly 0.5, reached at about 10^15 GeV). And high energies are where a coupling might naturally take a simple value like 1. So what if there's a brane model where the top yukawa is 1 in the far UV, for some relatively simple reason, and then it is also near 1 in the far IR, because of a UV/IR relation that we don't understand yet? String theory contains UV/IR relations (scroll halfway down for the discussion); none of them appear to be immediately applicable to this scenario; but such relations are far from being fully understood.

At the same time, I think of Christopher Hill's recent papers (1 2, it's basically the same paper twice), in which he first restricts the SM to just the top and the Higgs, and then considers a novel symmetry transformation, which he likens to a degenerate form of susy. At high scales he ends up with the relation that the Higgs quartic equals half of the square of the top yukawa - which is not what I'm looking for. Then again, he also ends up with Higgs mass equals top mass, with the difference to be produced by higher-order corrections. So perhaps his model, already twisted away from ordinary supersymmetry, can be twisted a little further to yield a Rodejohann-Zhang RG flow for the top yukawa, as well as a Shaposhnikov-Wetterich boundary condition for the Higgs quartic.

One might want to see whether this can all be embedded in something like the "minimal quiver standard model" (MQSM), which is not yet a brane model, but it is a sort of field theory that can arise as the low-energy limit of a brane model; and the MQSM is the simplest quiver model containing the SM.

Finally, to round things out, one might seek to realize the sbootstrap's own deviant "version of susy" here too, perhaps by using one of the brane-based "ideas for a model" already discussed in this thread.