### The particle spectrum predicted by TGD and TGD based SUSY

The detailed model of elementary particles has evolved slowly during more than 15 years and is still in progress. What SUSY means in TGD framework is second difficult question. In this problem text books provide no help since the SUSY differs in several respects from the standard SUSY.

**The general TGD based view about elementary particles**

A rough overall view about the particle spectrum predicted by TGD has remained rather stable since 1995 when I performed first p-adic mass calculations but several important ideas have emerged allowing to make the vision more detailed.

- The discovery of bosonic emergence had far reaching implications for both the formulation and interpretation of TGD. Bosonic emergence means that the basic building bricks of bosons are identifiable as wormhole contacts with throats carrying fermion and anti-fermion quantum numbers.
- A big step was the realization wormhole throats carry Kähler magnetic charge. This forces to assume that observed elementary particles are string like objects carrying opposite magnetic charges at the wormhole ends of magnetic flux tubes. The obvious idea is that weak massivation corresponds to the screening of weak charges by neutrino pairs at the second end of the flux tube.
At least for weak gauge bosons this would fix the length of the flux tube to be given by weak length scale. For fermions and gluons the length of flux tube could also correspond to Compton length: the second end would be invisible since it would contain only neutrino pair. In the case of quarks an attractive idea is that flux tubes carry color magnetic fluxes and connect valence quarks and have hadronic size scale.

There are thus several stringy length scales present. The most fundamental corresponds to wormhole contacts and to CP

_{2}length scale appearing in p-adic mass calculations and is analogous to the Planck scale characterizing string models. String like objects indeed appear at all levels in TGD Universe: one can say that strings emerge. The assumption that strings are fundamental objects would be a fatal error. - p-Adic massivation does not involve Higgs mechanism. The idea that Higgs provides longitudinal polarizations for gauge bosons is attractive, and its TGD based variant was that
*all*Higgs components become longitudinal polarizations so that also photon has a small mass. The recent formulation of gauge conditions as p_{M2}• ε=0, where p_{M2}is a projection of the momentum to to a preferred plane M^{2}⊂ M^{4}assignable to a given CD and defining rest system and spin quantization axis, allows three polarizations automatically. Also the construction of gauge bosons as wormhole contacts with fermion and anti-fermion at the ends of throat massless on mass-shell states implies that all gauge bosons must be massive. Therefore Higgs does not seem to serve its original purposes in TGD. - This does not however mean that Higgs like states - or more generally spin 0 particles, could not exist. Here one encounters the problem of formulating what the notions like "scalar" and "pseudo-scalar" defined in M
^{4}field theory mean when M^{4}is replaced with M^{4}× CP_{2}. The reason is that genuine scalars and pseudo-scalars in M^{4}× CP_{2}would correspond to lepto-quark states and chiral invariance implying separate conservation of quark and lepton numbers denies their existence.These problems are highly non-trivial, and depending on what one is willing to assume, one can have spin 0 particles which however need not have anything to do with Higgs.

- For a subset of these spin 0 particles the interpretation as 4 polarizations of gauge bosons in CP
_{2}direction is highly suggestive: the polarizations can be regarded as doublets 2 ⊕2* defining representations of u(2)⊂ su(3) in its complement and therefore being rather "Higgsy". Another subset consists of triplet and singlet representations for u(2)⊂ u(3) allowing interpretation as the analog of strong isospin symmetry in CP_{2}scale for the analogs of hadrons defined by wormhole contacts. - 3 ⊕ 1 representation of u(2) ⊂ su(3) acting on u(2) is highly analogous to (π,η) system and 2⊕2* representation assignable naturally to the complement of u(2) is analogous to kaon system. Exactly the same representations are obtained from the model of hadrons as string like objects and the two representations explain the difference between (π,η) like and (K,Kbar) systems in terms of SU(3) Lie-algebra. Also the vector bosons associated with pseudo-scalar mesons identified as string like objects have counterparts at the level of wormhole contacts. A surprisingly precise analogy between hadronic spectrum and the spectrum of elementary particle states emerges and could help to understand the details of elementary particle spectrum in TGD Universe.

In both cases charge matrices are expressible in terms of Killing vector fields of color isometries and gamma matrices or sigma matrices acting however on electroweak spin degrees of freedom so that a close connection between color and strong isospin is suggestive. This connection is empirically suggested also by the conserved vector current hypothesis and and partially conserved vector current hypothesis allowing to express strong interaction observables in terms of weak currents. In TGD framework color and electro-weak quantum numbers are therefore not totally unrelated as they are in standard model and it would be interesting to see whether this could allow to distinguish between TGD and standard model.

- For a subset of these spin 0 particles the interpretation as 4 polarizations of gauge bosons in CP

The detailed model for elementary particles involves still many un-certainties and in the following some suggestions allowing more detailed view are considered.

**What SUSY means in TGD framework?**

What SUSY means in TGD framework is second long-standing problem. In TGD framework SUSY is inherited from super-conformal symmetry at the level of WCW. The SUSY differs from * N*=1 SUSY of the MSSM and from the SUSY predicted by its generalization and by string models. One obtains the analog of the * N*=4 SUSY in bosonic sector but there are profound differences in the physical interpretation.

- One could understand SUSY in very general sense as an algebra of fermionic oscillator operators acting on vacuum states at partonic 2-surfaces. Oscillator operators are assignable to braids ends and generate fermionic many particle states. SUSY in this sense is badly broken and the algebra corresponds to rather large
*N*. The restriction to covariantly constant right-handed neutrinos (in CP_{2}degrees of freedom) gives rise to the counterpart of ordinary SUSY, which is more physically interesting at this moment. - Right handed neutrino and antineutrino are not Majorana fermions. This is necessary for separate conservation of lepton and baryon numbers. For fermions one obtains the analog
*N*=2 SUSY. - Bosonic emergence means the construction of bosons as bound states of fermions and anti-fermions at opposite throats of wormhole contact. This reduces TGD SUSY to that for fermions. This difference is fundamental and means deviation from the SUSY of
*N*=4 SUSY, where SUSY acts on gauge boson states. Bosonic representations are obtained as tensor products of representation assigned to the opposite throats of wormhole contacts. Further tensor products with representations associated with the wormhole ends of magnetic flux tubes are needed to construct physical particles. This represents a crucial difference with respect to standard approach, where one introduces at the fundamental level both fermions and bosons or gauge bosons as in*N*=4 SUSY. Fermionic*N*=2 representations are analogous to "short"*N*=4 representations for which one half of super-generators annihilates the states. - The introduction of both fermions and gauge bosons as fundamental particles leads in quantum gravity theories and string models to d=10 condition for the target space, spontaneous compactification, and eventually to the landscape catastrophe.
For a supersymmetric gauge theory (SYM) in d-dimensional Minkowski space the condition that the number of transversal polarization for gauge bosons given by d-2 equals to the number of fermionic states made of Majorana fermions gives d-2= 2

^{k}, since the the number of fermionic spinor components is always power of 2.This allows only d= 3,4,6,10,16,... Also the dimensions d+1 are actually possible since the number of spinor components for d and d+1 is same for d even. This is the standard argument leading to super-string models and M-theory. It it lost - or better to say, one gets rid of it - if the basic fields include only fermion fields and bosonic states are constructed as the tensor products of fermionic states. This is indeed the case in TGD, where spontaneous compactification plays no role and bosons are emergent.

- Spontaneous compactification leads in string model picture from
*N*=1 SUSY in say d=10 to*N*>1 SUSY in d=4 since the fermionic multiplet reduces to a direct sum of fermionic multiplets in d=4. In TGD imbedding space is not dynamical but fixed by internal consistency requirements, and also by the condition that the theory is consistent with the standard model symmetries. The identification of space-time as 4-surface makes the induced spinor field dynamical and the notion of many-sheeted space-time allows to circumvent the objections related to the fact that only 4 field like degrees of freedom are present.

## 2 Comments:

Hi, Matti

I notice today that Lubos is coming closer to some idea of things- a good try of defending his positions as natural (I think as I use the term natural dimensions ).

I mean on a natural sphere we can have three right angles, so on a plane we have four... basic finite arithmetic. So what is natural if his natural dimensions hide from reality our supernatural symmetries? Does science really address the God like fundamental mysteries- oh it is a cleaver reply and speculation.

But it brings me to two counter replies concerning the nature of symmetry in general and if we want some ultimate idea of universal balance- all of which takes place in theories like yours beyond the level of what is "naturally" discussed in limited old physics view.

For how can things be conserved otherwise, that is if they have no place for the return of arrows? This is to say that from a higher view it is still an open question if there can be some minimum idea at least as local to all systems, after all. One does not need some unnatural particles to explain the evidence suggested recently for dark matter in the early galaxies and it is certainly no evidence for the existence of say wimps.

So how can we resolve these views of a minimum and yet no minimum of say the Planck level of action volume etc, especially if both views apply and btw blows away the meaning of Lubos anthropocentric concerns?

If the last particle (unabashedly he calls the God particle) remains of a certain value but elusive then so will some scientific facts that could be there- which brings me to a similar thought on as you say the square root of the thermodynamics principle- I rather suspect that a more general idea, one beyond the simple quantum formalism by mathematical determinants and some implied field of gluons and so on as most of the mass in the momenta, that such things which of course relate to the wave equation probabilities of square values would certainly be at least the Mersene or p-adic roots, so I would expect you to say.

Now combinational approaches are important also in this issue of higher capacities in a loosely unified universe of relative energies as if a multiverse even of the oscillating or inflation kinds- such as seems the gravitational sources, simple or in depth. But even in early planet prediction the perturbations as such were naturally uncertain as coincidental or merely a way to show the influences so as to predict the discovery of planets so how good a principle is this to answer fundamental questions?

But I mention this especially in what the color means for the frequency and that you in a sense are closer in the continuous realm to Lubos than I as to what is natural, your take on these things where our Lubos is competent enough to try to resolve and defend his views.

The PeSla hoping you might enlighten me where I have all but abandoned the simple ideas of a quantum ground as the ultimate science.

Lubos as a physicist has achieved the so called "mature" phase humanly speaking too early. For the three periods in physicist's life see the cartoon

http://www.smbc-comics.com/index.php?db=comics&id=2556#comic .

Naturality in technical sense means that the parameters of the theory should be of order unity and that the fitting to experimental data should not require any fine tuning. Both GUTs and string theories face here formidable problems, which should tell to the theoretician that something is is profoundly wrong.

In particular, SUSY in the standard form was hoped to help to make theory more natural in the case of Higgs. LHC has in practice destroyed these dreams.

The deadly mistake is easy to identify. It is the assumption that elemetnary bosons are really elementary so that SUSY is realized at the fundamental level for gauge bosons: d-2 is the number of transversal polarizations and SUSY requires this to be power 2. This leads to critical dimensions: d=2,4,6,10,. d=10 leads to string models. The original dream was theory of everything but the outcome was landscape catastrophe.

The cure is simple and relies on the notion of bosonic emergence stating that elementary bosons are not so elementary but expressible as pairs of elementary fermions. Require SUSY only for the fundamental fermions) and induce it to the bosonic sector via emergence.

There is no need for Majorana fermions and separate conservation of B and L is possible. Possibility to identify SUSY generators as right handed neutrinos gives direct contact with standard model physics. This leads to a totally different view about SUSY consistent with experimental facts. It however seems that theoreticians will continue with old recipes for decade or two.

One could also generalize the naturality requirement: the theory should explain without any fine tuning the observed symmetries of nature which standard model seems to code. Why standard model gauge group and some other? The attempt to answer this question would lead to dramatic progress but again theoreticians refuse to make it since it would lead to conflict with string dogma.

Sad that fantastic developments are just around the corner but the egos of colleagues are too big to allow progress.

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