GRAND UNIFICATION H. Georgi

To cite this version:

H. Georgi. GRAND UNIFICATION. Journal de Physique Colloques, 1982, 43 (C3), pp.C3-705-C3- 721. ￿10.1051/jphyscol:1982384￿. ￿jpa-00221940￿

HAL Id: jpa-00221940 https://hal.archives-ouvertes.fr/jpa-00221940 Submitted on 1 Jan 1982

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CoZZoque C3, suppzdrnent au no 12, Tome 43, ddcernbre 1982 page C3-705

GRAND UNIFICATION

H. Georgi

Department of Physics, Lyman Laboratory of Physics, Harvard University, hl.4 02138, U.S.A.

Today I will talk about the progress that has been made in the last year or two in unifying the interactions of physics. The short summary is that there hasn't been any. This is a field which is strangling for want of experimental input. But some things have happened. If we haven't made progress, we have at least learned a thing or two. And who knows, they may turn out to be useful when experiment does finally point us in the right direction.

UNIFICATION OF OBSERVED INTERACTIONS

Let me begin by briefly discussing the unification of the observed (or almost observed) SU(3) xSU(2) xU(1) gauge interactions. Nothing revolutionary has happened lately,which is not surprising since the main theoretical ideas have been in place for 8 But there has been some evolution in our ideas. The most 2 interesting recent developments have been in the predictions of sin OW and of the 2 proton decay rate. The prediction of sin eW in the simplest SU(5) model has now been refined about as far as it is worth refining it.2 And it agrees perfectly with the data. At this point, improvement in the data would be most welcome. The situation with respect to proton decay is more interesting. On the theoretical side, two things have happened. One is that the experimental deter- mination of A has evolved. As David Politzer will discuss in the next talk, the QCD best (or at least the current favorite) value of A is something like 150 MeV, down a factor of two or more from earlier estimates. The second development is an improvement in the model estimates of the matrix elements involved in the proton decay process. It has been found3 that the three-quark fusion process, or the pole diagram cannot be ignored. The inclusion of this effect brings the results into agree- ment with results from complementary approaches (such as current algebra). But both the change in A and the extra diagram have the effect of increasing QCD the predicted proton decay rate in any given model. In the simplest SU(5) model, this brings the prediction to the very edge of disagreement with the present experi- mental bound. On the other hand, there are "candidate" nucleon decay events from the Kolar Gold Field and NUSEX group^.^ This is very exciting. Either we will see more soon, or the simplest (and thus one of the most attractive) GUTS will be ruled

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out.

SU(5) VERSUS SO(10)

Alas, it doesn't take much of a modification of the simplest GUT to drasti- cally increase the uncertainty in the prediction of the proton decay rate. In SU(5), many more light would increase the lifetime (although one extra family doesn't do,much). After SU(5), the next simplest GUT is based on an SO(10) gauge group. In SU(5), the unification scale is unique, because there is no larger subgroup of SU(5) that contains SU(3) xSU(2) xU(1). But in S0(10), there are many possible routes from the full SO(10) symmetry to SU(3) xSU(2) xU(1). Some of them involve several different scales and many more parameters than in SU(5) (see Table 1). In this theory (or perhaps I should say "set of theories") it is easy to change the proton decay rate prediction by a factor of almost 103 . Let's hope that Nature is Simple.

TABLE 1 SO(10) Breakdown Schemes Ref. T -P

+ SU(3) x SU(2) x U(1) = H

+ SU(5) + H

+ SU(5)' x U(l)(anti SU(5)) + H

-.SO(6) x SU(2) x U(1) + H

There has'also been a development in technical which has potentially extremely important application to GUTS. This is the suggestion by Rubakov and Callan (and the related work by Wilczek) that SU(5) monopoles may catalyze baryon number violating processes with a typical strong interaction cross section.* I say "potentially important" only because I do not fully understand the argument. If it is correct, it is certainly one of the most exciting ideas to come along in some time.

THE GRAND MYSTERIES

There may be good reasons to embellish the simple SU(5) GUT. Although the SU(3) xSU(2) xU(1) interactions of and fit into SU(5) like the proverbial hand into a (fivc fingered) glove, this unification does little to demystify two old puzzles: hierarchy and flavor. The large scales, the Planck H. Georgi

mass % and the grand unification scale MG are so much larger than the small scales Mu, AQCD and quark and masses--the hand is at the end of a very, very long arm. And why is ttgere more than one generation of quarks and leptons? Isn't one hand enough? Some things get less mysterious with time, simply because we get used to them. We have grown accustomed to , confinement, even income tax laws. But hierarchy and flavor seem more mysterious as time passes, because our attempts to understand them don't seem to lead anywhere.

UNIFICATION OF IMAGINED INTERACTIONS

Here I will discuss three types of unobserved interactions which, if they exist, might help unravel these puzzles: Technicolor, and Family Symmetry. All of these subjects go far beyond grand unification, but I will talk only about those aspects which impinge on GUTS and the hierarchy and flavor puzzles. Technicolor and Supersymmetry might address the hierarchy puzzle while Family Symmetry may have something to do with flavor.

TECHNICOLOR

It is easy to understand why M >>%if the W mass is due to dynamical breaking of the SU(2) xU(1) symmetry. If there is a technicolor (TC) interaction of (as yet unobserved) technifermions. weak at MG, MW may be -eATC/sin8 where ATC is the analog of A for the technicolor intera~tion.~This is automatically exponen- OCD tially small compared to MG. This kind of dynamical mechanism for breaking SU(2)xU(l) almost surely makes sense, because it is based on a simple and direct analogy with chiral symmetry breaking in QCD. It is very simple and elegant. And it requires no fundamental Higgs mesons with masses less than M This is impor- G' cant, because in ordinary quantum field theories, it takes one unnatural finetuning for each Higgs multiplet that must be kept light. The trouble with TC is that by itself, it cannot give quark and lepton masses. There must be other interactions, called extended technicolor, ETC, which couple quarks and leptons to techni- fermions.1° Of course, if TC is embedded in a GUT, there are other interactions. But since these are interactions with particles of mass "M if TC is asymptotically G' free (AF), they don't do much. It would seem that there are four possibilities for implementing ETC: Have spinless bosons with a mass *METC not much larger than A ' (a) TC' (b) Have gauge bosons with a mass -M ETC .' (c) Give up the of TC and push up METC; (d) Rely on interactions at MG. It is easy to construct realistic models in (a), but this possibility is very unattractive because it requires fine tunings to keep the spinless bosons light. The most of the motivation for TC is lost. JOURNAL DE PHYSIQUE

(b) is the classic ETC idea. It requires no light scalars. It is very ambitious. A successful grand unified ETC scheme would describe all of low energy in terns of a small number of gauge coupling constants. The problem is that it is hard, and perhaps impossible, to get enough structure. And there are phenomenological difficulties. General arguments (supported by toy examples) suggest that these ETC models will have potentially serious flavor changing neutral current interactions. l1 Not much has happened recently to suggest that these difficulties can be overcome with AF TC. (c) has its roots in Holdom's comment that if the TC theory were a confining phase of a non AF theory with a nontrivial (UVFP), the %TC scale could be raised and the phenomenological problems with ETC correspondingly allayed.12 But it is still hard to build realistic models. (d) is the suggestion by Glashow and me.that if we could raise M to MG, we wouldn't need ETC in the ETC usual sense at all, but could use the heavy spinless mesons which always appear in GUTS to produce quark and lepton mass.13 Ian MacArthur and I then found a plausible 14 dynamical scheme that could give the right physics. Briefly, the idea is in the confining phase, a TC theory with a nontrivial UVFP might be equivalent to an AF effective TC (eTC) theory with fundamental Higgs scalars coupled to the techni- fermions. In this effective theory, the scalar would be light for dynamical reasons. Assuming that this idea is correct, I was able to construct a realistic 5 15 GUT based on an SO(10) symmetry. Unfortunately, while this realization of the eTC idea has some interesting features,16 it seems unreasonably complicated and contrived. Even if eTC works just as I expect, it seems hard to build a compelling model.17 Something is obviously still missing. But the TC direction is not (I think) ruled out entirely. It is still an attractive idea, and technifemions should be one of the primary quarries for the future generation of accelerators.

SUPERSYMMETRY

Supersymmetry (SS) has been discussed extensively in the parallel session devoted to it and in Fayet's talk. Here I will discuss only a very specific appli- cation of supersymmetry, to the hierarchy puzzle in GUTS. One can imagine various ways in which supersymmetry might solve the fine tuning problem of keeping Higgs doublets much lighter than the unification scale. The simplest and least subtle possibility is to have the fennion superpartners of the Higgs carry an unbroken chiral symmetry. But it is al.so possible to make use of so called "supermiracles"(which Fayet called nonrenormalization theorems). If the Higgs doublet is massless in tree approximation, it stays massless until the super- symmetry is broken. Thus all we need do is to avoid fine tuning in the tree ap- 19,20 proximation.18 This can be done in several ways. It is not so obvious how SS can help with the explanation of the large ratio of H. Georgi

MG to \. At fii-st it was hoped that TC and SS could be combined into "supercolor". Dimopoulos and Raby and Dine, Fischler and Srednicki constructed models in which they hoped that the small scale would be produced by the dynaaical breaking of 21 supersymmetry. There are arguments which suggest that this kind of dynamical SS breaking will 23 not work." But Witten has invented another way of getting a large hierarchy. Introduce the small scale explicitly in an OIRaifeartaigh model which spontaneously breaks SS at -1 TeV, but in such a way that the large scale is completely undeter- mined in tree approximation. Witten showed that radiative corrections can produce an exponentially large (VEV). This is the so called "inverted" or "backwards" hierarchy in which the small scale is fundamental and the large scale is dynamically induced. There are several practical difficulties with the inverted hierarchy. One must be careful not to break the gauge symmetry at the large scale down beyond SU(3) xSU(2) xU(1). This is not trivial because the large scale symmetry breakdown is driven by the symmetry breaking at 1 TeV which respects only SU(3) xU(1). There is a tendency for SS breaking in these theories to "decouple", which means that only the very heavy, mass -M particles fell SS breaking in tree approximation. The G' effects of on light particles is suppressed, of order VMG. Then the superpartners of the observed particles are not sufficiently heavy to have escaped detection. Finally, thr.re are often many light supermultiplets in such theories, often so many that the gauge couplings get very large before unification. The first two of these problems are eliminated if the SS breaking scale is p " q. In such a so-called geometric hierarchy model, decoupling is a virtue, 2 because the effect of SS breaking on the light particles is of order U /M M G - W' Still, despite some clever model building by Dimopoulos and ~ab~,~~no totally satisfactory backwards geometric hierarchy model has been constructed. This is basically because spontaneous supersymmetry breaking is very cumbersome. Sakai and Dimopoulos and I two years ago demonstrated that it is easy to build realistic GUTS in which the SS is softly broken at 1 T~v.'~These early efforts did not address the question of the large scale difference. But in the last few weeks, Dimopoulos and I have disoovered that an inverted hierarchy can be driven by soft SS breaking at 1 TeV .26 The idea is that if the supersymmetric vacuum has degeneracies associated with scale transformations, the soft SS breaking terms can destabilize the vacuum, leading to a tree approximation Hamiltonian which is unbounded below. Classically there are tachyons and the theory is sick. Quantum corrections (proportional tc the soft breaking) can restabilize the vacuum for large values of the VEVs, thus resuscitating the classically sick theory. Amazingly enough, this effect, which we call QMR, for "quantum mechanical resuscitation",can all happen in the regime of validity of perturbation theory. It is straightforward to construct realistic models based on this idea JOURNAL DE PHYSIQUE

Dimopoulos described two types in his talk in the parallel session on Unified Gauge Theories. Neither requires any fine tuning of parameters of order M The G' only unnaturalness involves low energy parameters. When we break the SS softly, we must take care to preserve a super GLM mechanism, for example by adding the same soft breaking terms for each family of quarks and leptons. The problem with this is that it is not natural in the models we have constructed. The soft breaking terms are renormalized differently. But we expect that this embarrassment can be avoided in models in which multiple families appear naturally. So far, I haven't mentioned gravity. That's because it is best to think about inverted hierarchies while standing on your head, which is easier if you turn off gravity. But there is a philosophical problem here. In a TC model, it may make sense to ignore gravity. 5 is bigger than the fundamental scale M but not so G' much bigger that the ratio %/MG is embarrassingly large. But if the small scale p) is % (or the geometric scale is fundamental as in an inverted hierarchy, and M G dynamically induced, then unless Mp is also dynamically induced, there is still a hierarchy puzzle. Why is Mp >>\? Thus we should really build inverted hierarchy models in which gravity is included, and M and M are necessarily about equal. P G These words are spoken trippingly on the tongue. But it is not so easy to assign them any meaning. It may be interesting to note, however, that the inverted hierarchy models do not seem to suffer from the cosmological problem pointed out by ~einberg.~'He found that terms in the effective potential induced by gravity and proportional to the superpotential tend to drive the theory into the wrong vacuum. But in classically scale invariant supersymmetric theories, the superpotential vanishes for all vacua. That is probably enough to eliminate,the problem. There is a right-side-up approach to the hierarchy puzzle in a SS theory, in

which the ratio %/M~ is just a large power of a small . 28 The idea is to break SS at MG, but arrange the theory so that SS percolates into the interesting sectors of the theory only in high order processes. The original SU(5) model is so simple and elegant that it has to be right--at least part of the truth. I thought so eight years ago when I first wrote it down, and I still think so today. None of the solutions I have discussed to the hierarchy puzzle have that character. But that doesn't mean that they are all wrong. Just that we don't have enough of the picture to see it clearly. We need some guidance from experiment. Where should we look? All these models predict new types of heavy elementary particles in the TeV region. It seems impossible to get a natural hierarchy without them. Eventually, this will be very interesting. But probably of more immediate interest is the different predictions of these models for pro ton decay. 5 There are no real examples of ETC GUTS, but in my SO(10) ETC model, proton decay is similar to that in the simplest SU(5) model. H. Georgi

The supersymmetric models are very different. The unification scale M in SS G GUTS is typically larger by an order of magnitude or so than the scale in an analogous non SS theory. The difference is the light gauge fermions, which 29 decrease the rate at which the SU(3), SU(2) and U(1) coupling constants converge. The old M could be restored if a pair charge '1, SU(2) xSU(3) singlet super- G multiplets remain light below nF.30 but 1 cannot think of 9 reason why this should occur. Thus I expect that if supersymmetry is unbroken below M the usual G' exchange contribution will be so suppressed as to be inaccessible experimentally (and therefore boring). For example, in the SU(6) model built by Dimopoulos and me, the proton lifetime is something like years. Two things can happen tc change this picture. Supersymmetric theories can violate baryon number in a different way, so that the proton lifetime is propor- tional to only two powers of MG, not four as in the nonsupersymmetric SU(5) model.31 The difference is the existence of scalar partners of the light particles which allows baryon number violating dimension 5 operators in the effective low 0- energy theory. These can lead to proton decay into K+; (and N-tK V) at an observable rate in some theories.32 This doesn't happen, however, in theories (like the SU(6) model above) in which the Higgs doublet supermultiplets are light because they carry a chiral symmetry which is unbroken at M G' In the intermediate scale backwards hierarchy model of Dimopoulos and Raby, proton decay occurs due to scalar boson exchange.24 This is much more important (in this model) than gauge boson exchange because the color triplet scalars in the 5 and 5 get a mass of the order of the intermediate scale, rather than MG. Scalar +- 0 + triplet exchange causes proton decay primarily into K v or K p , because the !J Higgs multiplets couple more to heavier particles. 0 + Thus if proton decay is seen with ~re as the primary decay mode, it is reasonable to assume that supersymmetry (if it is relevant at all) is broken at M G or M . On the other hand, if the limit on the proton lifetime is pushed beyond 1033Pyears or so, or if the rate is years and the dominant modes involve K's, then some form of low energy supersymmetry may be the most reasonable explanation.

I should stress that in none of these models is there a firm prediction for T P' All of them have many more parameters which go into T P than simple SU(5).

FAMILY SYMMETRY

The family puzzle, at least to me, is even more mysterious than the hierarchy puzzle. Here many ideas have been tried, some of which seemed quite clever and interesting at the outset. But none of them have led anywhere, or at least not to anything we can recognize as progress without more experimental guidance. Still it may be useful to recount here this frustrating history. Some of it may even be right, for reasons which we dc not yet see clearly. At any rate, it may serve to steer people away from stale, flat and unprofitable directions. JOURNAL DE PHYSIQUE

I should say that there is one fashionable approach to the flavor puzzle that I will not discuss--the notion of composite quarks and leptons. I won't talk about it here because it doesn't seem to have much to do with unification (indeed, many of these models undo even the partial unification of SU(2) xU(1)). For what it is worth, though, I think that sensible models of this kind33 will not lead to any real improvement in our understanding of flavor, because they will be at least as complicated and arbitrary as the multiple families they seek to explain. I will organize the discussion of approaches to the family question in three broad categories: Discrete unification, unitary unification and orthogonal unification. All of the schemes that I discuss will involve complex representa- tions of the unifying group. Only if the representation of the Weyl fermions is complex can the gauge interactions naturally distinguish fermions with V-A interactions from those with V+A weak interactions. All the quarks and leptons we have seen so far are clearly V-A. Some workers, such as Pati, Salam, and Strathdee, build models which have real representations, so that they have "mirror fermions" with the wrong handedness for the ^.^^ This technically possible. But if it is right, then nature has been deliberately mis- leading us in exposing only those quarks and leptons with V-A weak interactions. The primary enemy of any deep understanding of flavors is the Glashow, Iliopoulos, Maiani (GIM) mechanism. 35 This wonderful mechanism for suppressing flavor changing neutral current effects works when the gauge interactions act the same way on each family. Of course at low energies, this seems to be the case. The SU(3) xSU(2) xU(1) gauge interactions do not distinguish between the different families. If, on the other hand, there are additional gauge interactions which act differently on the different families, the family puzzle will be a lot less puzzling. It is the gauge symmetries associated with these hypothetical gauge interactions that I refer to as family symmetry. The role of these interactions is to eliminate the GIM mechanism and distin- guish the different families. It follows that they produce flavor changing neutral current effects. We know that these effects are very weak, and thus we know that the family symmetries (if they exist) are broken at an energy higher than the 300 GeV of SU(2) xU(1) breaking. How much higher we do not know. If the family symmetries are broken at M they are not very interesting phenomenologically. G' But it is possible that they persist down to lower energies, in which case they may produce observable flavor changing neutral current effects. Experiments to see rare decay modes produced by such interactions must not be forgotten in our rush to - + higher energy and more exotic processes. The discovery (for example) of KL->lJ e would be just as important as (say) N-N mixing. And I think that the former is much more likely to exist at an observable rate. 0ne.very amusing suggestion is that the observed CP violation in the K meson system may arise from such GIM violating interaction^.^^ This gives a much more nearly superweak theory of CP violation than the standard six quark SU(2) xU(1) H. Georgi

model. For example, failure to observe E'/E at the level predicted by Gilman and might constitute evidence for new interactions of this kind.

DISCRFPE UNIFICATION

Here the idea is that there may be a family symmetry group with the same structure as the ordinary unifying group, for example SU(5), and that the full symmetry is a product of the two with a discrete symmetry under which the factors are interchanged. A simple example is a five family model in which the LH fermions transform under SU(5) x SU(5) like (10,5)+(5,10)+(5,5), where the first factor is ordinary SU(5) and the second is a "family SU(5)". This is typical of such models in that it has fermions, in this case five 5's and five 5's which get an SU(3) xSU(2) xU(1) invariant mass of the order of the family symmetry breaking scale, Only the five 10's and five of the 5's survive below M to form five F ordinary families with V-A weak interactions. Ramond has had some fun imagining what happens if some of the "heavy" parti- cles with mass of order % are actually light for dynamical or just plain acci- dental reasons.38 For example, the SU(2) doublets in the heavy 5's are really split electromagnetically.

UNITARY FLAVOR UNIFICATION

It is also possible to embed both SU(5) and family symmetry into a single simple unitary group.39 An example is my SU(11) model in which --- SU(11) +SU(5) xSU(~)~~~~~~and the LH fermions are 330 +I65 +55 +11 (these are SU(11) tensors with 4 upper indices and 3, 2 and 1 lower indices respectively). When the dust settles in this model, there are three normal families plus heavy stuff. Of course, there 2 a lot of dust. So much that some of the family symmetry must be broken at very high energy, at or near MG, to prevent the ordinary coupling constants from getting large before unification. Discrete and unitary unification are amusing numerological games. But there is obviously something missing. There is just no compelling reason to prefer any one of these models over all the others. But that could change. For example, we might find some theoretical context in which some particular type of representation looks especially appealing. At any rate, keep looking for those rare decay modes. The GLM mechanism is bound to break dcwn. The only question is "Where?" and "How Much?"

ORTHOGONAL UNIFICATION

The last unification of family symmetry that I will discuss is based on the simplest and most appealing idea: that all the fermions might be described by a single spinor representation (SR) of an orthogonal group. This sounds great JOURNAL DE PHYSIQUE

initially, since a single family fits well into the 16 dimensional SR of s)(10). And the SRs of the larger orthogonals are built out of copies of SRs of smaller ones. It is not so simple though, because all larger orthogonal groups have as many 16's as 16's in their SRs, and thus as many quarks and leptons with V+A weak interactions as with V-A weak interactions. Unless we want to degenerate to a mirror scheme, we need something to distinguish the two. This is possible for S0(4n+2) which has complex SRs. The obvious possibility is technicolor. For example, technicolor SU(2) can be embedded in SO(14) so that the SR consists of two normal families and a technicolor doublet of V+A families. This is the Farhi- Susskind model.40 Here the TC is no good for solving the hierarchy puzzle because it is not sufficiently AF. 4 1 The SO(18) SR can give three normal families with a technicolor S0(5)(=Sp(4)). Alas, there are so many fermions in the SR (8 V-A and 8 V+A families) that the gauge couplings get very large before unification. Perturbative unification is 2 lost and the apparent success of the sin OW prediction would have to be regarded as accidental. Still, this model is appealing. No doubt, there will be further attempts to make it work. Larger unitary groups are even worse. The trouble is that only the S0(4n+2) groups have complex SRs, and when n increases by 1, the size of the SR increases by a factor of 4. They get worse exponentially.

FUNNY CHARGES

All the extra gauge symmetries I have discussed so far have been trivial extensions of SU(5) in the sense that all of the low energy SU(3) xSU(2) xU(1) resided in the SU(5) subgroup. But lots more bizarre embeddings of SU(3) xSU(2) x U(1) are possible. In general, if you do something bizarre, you get a theory that doesn't make sense because your fermions are not even real under SU(3) xU(1). This mucks up QED and QCD. But the SRs of the S0(4n+2) groups are almost real, and it is very easy to make it work. To me, the most amusing example of a nontrivial embedding is Kim's SO(14) (or SU(7)) In the single SR in Kim's model, there are two normal V-A families but the two V+A families are displaced by one unit in charge in opposite directions. This produces another lepton doublet with normal V-A interactions because one of the V+A lepton douhlet with funny charge can be reinterpreted as an antilepton doublet. Thus there is room in the model for the T, as well as for the e and the U. Very clever! The funny charges also muck up coupling constant renormalization. To get an 2 acceptable sin OW, you must preserve an SU(4) xSU(3) subgroup unbroken down to low energies. All of what eventually becomes electric charge resides in this semi- simple SU(4) xSU(3) subgroup. Thus the monopoles in this model are light. This is another amusing feature of the model. Alas, the Kim model with a single SR is already ruled out by experiment. The H. Georgi

b quark in this model is peculiar. It is (at least) primarily part of a V+A SU(2) doublet with charges -113 and -413. Manohar has shokm that data on b decay from CESR, together with what we know from coupling constant renormalization and the stability of the proton, is not consistent with the Of course, one could always use two SR's instead of one, but then you give up the nicest feature, so why bother. Finally, I will mention a peculiar variant of the Kim model proposed to account for the alleged observation of fractionally charged particles.44 In the SR of S0(14), one can displace the V+A families by an '113 unit of charge, producing a host of colorless particles with charges '213, '113, etc. Goldberg has worked out an entertaining cosmological and astrophysical scenario in which these fractionally charged particles annihilate in early supernovae enough to be present today only in 45 the very small concentration which may have been observed. Finally, let me note that by enlarging the low energy symmetry group to contain an extra unbroken U(1) factor, so that there is a funny photon which does not couple to normal matter, one can build orthogonal unifications which simultaneously describe fractionally charged color singlet particles magnetic 46 monopoles with Dirac's value for the magnetic charge.

INVISIBLE AXIONS

I next turn to the history of an odd chapter in particle theory: the story of the Invisible Axion. The axion was an attractive solution to the puzzle of why CP violation in QCD is so small. The idea was to build a theory in which all the interactions in the SU(3) xSU(2) xU(1) theory except QCD instanton effects had a Peccei-Quinn (PQ) symmetry which changed the phase of the determinant of the quark mass matrix.47 Then there is a pseudo-, (PGB) the a~ion.~~The VEV of the axion adjusts itself to make the strong CP violation small. Trouble was the axion wasn't there. If it had been a PGB associated with SU(2) xU(1) breaking, as originally predicted,it should have had interactions suppressed by appropriate powers of G and should have shown up in various F' experiments. These experimental difficulties can be avoided if the axion is associated with 49,50 a higher symmetry breaking scale, because its couplings would be weaker. But lots of people realized that in the context of SU(3) xSU(2)xU(1), Kim's solution was really just trading one problem for another. The VEV which breaks the PQ symmetry had to be larger than 10' GeV to avoid problems with axion emission from the cores of hot stars.51 But then the large scale is so much larger than % that there is a hierarchy. But when the idea is adapted to GUTS it really looks nice, because the PQ symmetry can be broken at the GUT scale which is known to be large anyway. This gives the invisible axion: with couplings suppressed by powers 50.52 of MC, it can't be seen in any conventional particle physics experiments. The JOURNAL DE PHYSIQUE

PQ symmetry can be imposed by hand, but it is also possible to construct theories in which the PQ symmetry is "automatic" in the sense that it follows from the gauge 5 3 structure and renormalizability of the theory. The invisible axion is antiphysics, in a way, because you can't see it directly. It is, therefore, not too disappointing that there are cosmological difficulties associated with theories of this kind. Sikivie started us thinking about cosmological properties of invisible axions by pointing out that many such models have several degenerate vacua. This can lead to formation of different domains in the early universe, separated by domain walls 54 which foul up standard cosmology. This problem (if it is a problem) is easy to fix. Many people suggested ways to fix any theory to make the vacuum unique.55 The solutions are interesting only because none of them involve simple replication of identical families. It is even possible, in family symmetry theories, to find models in which the PQ symmetry is 56 automatic and in which there are no domains. But recently Preskill, Wise and Wilczek and Abbott and Sikivie have identified a cosmological problem which seems to be more difficult to exorcize.57 I call it the Axion energy crisis. They note that when the chiral symmetry breaking phase transition in QCD occurs, at a temperature of about a GeV, the axion fjeld in any given region has some random vacuum value, left over from the earlier history of the universe. In general, this value will not be near the minimum of the PQ symmetry breaking potential, which is the true VEV. A normal field would quickly settle down tc, the minimum, losing its extra potential energy by producing particles and reheating the universe. But here, the same weakness of couplings which makes the axion invisible makes this process slow compared to the expansion of the universe. The result is that the axion just sits there and loses energy to expansion. Unless the field is close to its VEV by accident, the resulting universe is dominated by the energy in the excited axion field. It closes the universe by many orders of magnitude. Thus the axion energy crisis is that the axion field in general has too much energy and cannot get rid of it. If this problem is as serious as it sounds to me, we will have to give up the invisible &ion or substantially modify it. That is not such a bad thing. The alternatives may be more experimentally accessible. Before closing let me return briefly to the unification of gravity. Frankly, I believe that the uniftcation of gravity is premature. Contemporary theories of are probably analogous to the four-fermion theory of charged current weak interactions; a useful description at distances large compared to the appropriate scale, but irrelevant at shorter distances. If so, trying to unify gravity and particle forces is like trying to unify electromagnetism with the Fermi theory. It will have to wait until we push our understanding of gravity down to shorter distances. H. Georgi

One suggestion in this direction is "induced gravity", in which the short distance theory is classically scale invariant, and Newton's constant is dynamically induced.58 Personally, I suspect that even wilder ideas are going to be required, perhaps the kind of theory conjured up by Holgar Nielsen, in which Lorentz invariance (and perhaps general coordinate invariance) is only approximate, valid at long distances but violated at shorter distance^.^' These theories do not yet exist, but perhaps the discipline of unification can help us to find them. There is one popular attempt to unify gravity with particle forces in the context of supersymmetry. This is N=8 .60 I think that the motivation for this is as follows. In conventional renormalizable gauge theories, one has a series of discrete and continuous choices to make. One must choose gauge group, fermion and boson representations, and usually many coupling constants. On the other hand, one can argue that the N=8 supergravity is the unique supersymmetric unification of s in stein's gravity and particle forces. Unfortunately, this uniqueness is its only obvious virtue. While the classical field theory presumably makes sense, it is not at all clear that there is a corresponding quantum theory. Even if it makes sense, it is not clear how to extract any information about the world from it. There have been attempts to extract information about particle interactions 61 below % using symmetry c~nsiderationsalone, finessing all the dynamical details. Even this doesn't appear to work.62 The spin 1. 1/2, and 0 states seem to be too intimately mixed up with higher spin states to survive at low energies and give a sensible description of particle physics. It seems to me that this is too high a price to pay for uniqueness. I would rather be able to calculate everything in terms of 23 parameters than to be able to calculate nothing in terms of two parameters. I will close with a parable which I learned from Alvaro De ~Gjula. Consider the similarities and differences between the following two sets: A farmer, his pig and truffles on the one hand and the theorist, the experimentor and discoveries on the other. The situation is this. The farmer leads his pig into the woods. The pig sniffs and roots around until he finds the truffles. Then the farmer hits the pig over the head with a stick and takes the truffles away. These are the simi- larities. The difference is that the forest into which the farmer leads the pig always contains truffles. This is the nature of the game. I can't tell you whether the best place to look for the next important clue is in proton decay, rare meson or lepton decay modes, new heavy particles, or whatever. Generally, you only find out whether you have found the crucial piece to a puzzle after you have been hit over the head with a stick. But keep looking. Otherwise, particle physics degenerates into philosophy. After all there is another difference between truffles and discov- eries. To the farmer and to the pig, truffles are only a luxury. JOURNAL DE PHYSIQUE

REFERENCES I. Georgi, H. and Glashow, S.L., Phys. Rev, Lett. 32 (1974) 438. Pati, J.C. and Salam, A., Phys. Rev. Dg (1974) 275. The grand unified model described in this paper is based on a peculiar version of strong interactions in which color SU(3) is broken and quarks have integral charge, but it can be adapted to the . See, also, Pati, J.C. and Salam, A., Phys. Rev. Dg (1973) 1240. No grand unified model is constructed in this paper, but some aspects of grand unification are anticipated in the introduction. Georgi, H.. Quinn, H.R. and Weinberg, S., Phys. Rev. Lett. 2 (1974) 451. Georgi, H. Particles and Fields, 1974 (APS/DPF Williamsburg ), ed. Carlson, C.E. (AIP, New York, 1975). I am fairly certain that I was the first to find the SO(10) model, because I dis- covered it a few hours before realizing that a simpler unification could be obtained in SU(5). Glashow and I chose not to incluee SO(1O) as a footnote in the SU(5) paper. It was discovered independently by Fritzsch, H. and Minkowski, P., Ann. of Phys. 93 (1975) 193, and I suspect also by Pati, J. and Salam, A. (private communication). Marciano, W.J. and Sirlin, A., Phys. Rev. Letters 46 (1981) 163; Dawson, S., Hagelin, J. and Hall, J., Phys. Rev. Dz(1981) 2666; see also the talk by Wheater, J. in the parallel session on Unified Theories, and references therein. Berezinsky, V.S., Ioffe, B.L., and Kogan, Ya. I., Phys. Lett. EB(1981) 33; Isgur, N. and Wise, M.B., Phys. Lett. B., to be published; Donoghue. J. and Golowich, G., Phys. Rev. D., to be published. Fernandex de Labastida, J.M. and Yndurain, F.J., Phys. Rev. Lett. 47 (1981) 101; Tomozawa, Y., Phys. Rev. Lett. 46 (1981) 463. See the parallel session on proton decay. De ~Gjula,A., Georgi, H. and Glashow, S.L., Phys. Rev. Lett. 45 (1980) 413; Barr, S., Phys. Lett. B., to be published. Georgi, H. and Nanopoulos, D.V., Nucl. Phys. BH(1979) 16. This pattern is associated with the partially unified SU(4) xSU(2) xSU(2) L R model of Pati and Salam; Pati, J. and Salam, Phys. Rev. Dg (1973) 1240, which was incorporated into a unified theory by the same group in Phys. Rev. Ds (1974) 275. Here there is enough freedom to have the extra U(1) survive down to low energies and contribute to neutral current phenomena. The neutral current predictions then depend on several parameters instead of none, as in SU(5). A pretty analysis of this ugly idea has been given by Barger, V., et al., Univ. of Wisconsin-Madison preprint MAD/PH/~~and 59 (1982). See other references therein. Rubakov, V.A., Academy of Sciences, U.S.S.R., Inst. for Nuclear Research preprint P-0211, Moscow 1981; Callan, C., Princeton preprints. Susskind, L., Phys. Rev. Ds, (1979) 2619. See, also, the review by Farhi, E. and Susskind, L., Physics Reports 74 (1981) 277. Weinberg, S., Phys. Rev. Ds (1976) 974 and DE (1979) 1277. H. Georgi

Dimopoulos, S. and Susskind, L., Nucl. Phys. BE(1979) 237; Eichten, E. and Lane, K., Phys. Lett. EB (1980) 125. Dimopoulos, S. and Ellis, J., Nucl. Phys. BE(1981) 505. Holdom, R., Phys. Rev. Ds(1981) 1441. Georgi, H. and Glashow, S.L., Phys. Rev. Lett. 47 (1981) 1511. Georgi, H. and MacArthur, Nucl. Phys. B., to be published. Georgi, H., Nucl. Phys. B., to be published. Manohar, A., Phys. Lett. gB(1982) 253. Axenides, M., Cox, P. and Yildiz, A., Phys. Rev. Lett. 3 (1982) 262. Witten, E., Nucl. Phys. Bz(1981) 513; see, also, Fayet's talk. Dimopoulos, S. and Wilczek, F., Santa Barbara preprint (1981). Grinstein, B., Phys. Lett. B, to be published; Cahn, R.N., Hall, L.J. and Hinchcliffe, I., Phys. Lett. XB(1982) 426. Dimopoulos, S. and Raby, S., Nucl. Phys. Bs(1981) 353; Dine, M., Fischler, W., and Srednicki, M., Nucl. Phys. Bs(1981) 575. Witten, E., Nucl. Phys. BE(1982) 253. Witten, E., Phys. Lert. 1058 (1981) 267. Dimopoulos, S. and Raby, S., Nucl. Phys. B., to be published. Dimopoulos, S. and Georgi, H., Nucl. Phys. Bm (1981) 150; Sakai, 2. Phys. Cc(1981) 153. Dimopoulos, S. and Georgi, H., Phys. Lett. B., to be published. Weinberg, S., Phys. Rev. Lett. 3 (1982) 1776. See, also, Arnowitt, R., Chamseddine, A.H. and Nath, P., Phys. Lett. B., to be published. Ibanez, L. and Ross, G.G., Phys. Lett. eB(1981) 439. Dimopoulos, S., Raby, S., and Wilczek, F., Phys. Rev. D2(1981) 1681. See, also, Einhorn, M.B. and Jones, D.R.T., Nucl. Phys. BE(1982) 475. Igarashi, Y., et al., Dortmund preprint DO-TH 82/09: Masiero, A., et al, Max- Planck preprint MPI-PAEfPTh 29/82. Sakai, N. and Yanagida, T., Nucl. Phys. BE(1982) 533; Weinberg, S., Phys. Rev. DE (1982) 257. Dimopoulos, S., Raby, S., and Wilczek, F., Phys. Lett. mB (1982) 133. See, also, Masiero, A., et al., CERN preprint TH 3298. See J. Preskill's talk to the parallel session on Composite Models. See, for example, Pati, J., Salam, A., and Strathdee, J.. Phys. Lett. EB (1982) 121. Glashow, S., Iliopoulos, J., and Maiani, L., Phys. Rev. DZ (1970) 1285. Davidson, A. and Wali, K.C., Phys. Rev. Lett. 46 (1981) 691. See, also, Zoupanos, G., Nat. Tech. Univ. Athens preprint and references therein. Gilman, F.J. and Wise, M.J., Phys. Lett. ZB (1980) 129. Ramond, P. in Grand Unified Theories and Related Topics (World Scientific Pub. Singapore, 1981) p. 65.. C3-720 JOURNAL DE PHYSIQUE

Georgi, H., Nucl. Phys. B= (1979) 126. Farhi, E. and Susskind, L., Phys. Rev. Dz(1979) 3404. Georgi, H. and Witten, E., unpublished. Gell-Mann, M., Raymond, P., and Slansky, R., in Supergravity, ed. by van Nieuwenhuizen, P. and Freedman, D. (North-Holland, 1979): Wilczek. F. and Zee, A. in Grand Unified Theories and Related Topics (World Scientific Pub., Singapore, 1981) p. 143. Kim, J.E., Phys. Rev. Lett. 45 (1980) 1916 and Phys. Rev. DC(1981) 2706. Manohar, A., Phys. Lett. B., to be published. Umemura, I. and Yamamoto, K., Prog. Theor. Phys. 66 (1980) 278, 66 (1981) 1430 and Phys. Lett. mB (1981) 34; Goldberg, H., Kephart, T.W., and Vaugh, M.T., Phys. Rev. Lett. 47 (1981) 1429; Li, L.-F. and Wilczek, F., Phys. Lett. XB (1981) 64. Goldberg, H., Phys. Rev. Lett. 3 (1982) 1518. Strominger, A,, Inst. Adv. Study preprint (1982); Georgi, H. and Preskill, J., unpublished. Peccei, R. and Quinn, H.R., Phys. Rev. Lett. 38 (1977) 1440. Weinberg, S., Phys. Rev. Lett. 40 (1978) 223: Wilczek, F., Phys. Rev. Lett. 3

Kim, J., Phys. Rev. Lett. 43 (1979) 103 Zhitnitskii, A.P., Sov. J. Nucl. Phys. 21 (1980) 260; Dine, M., Fischler, W., and Srednicki, M.. Phys. Lett. BE(1981) 409. Dicus, D.A., et al., Phys. Xev. Dg <1972) 1829. Wise, M.B., Georgi, H., and Glashow, S.L., Phys. Rev. Lett. 41 (1981) 402: Nilles, P., and Raby, S., Phys. Lett. B., to be published. Georgi, H., Hall, L.,and Wise, M.B., Nucl. Phys. BE(1981) 409. Sikivie, P., Phys. Rev. Lett. 48 (1982) 1156. Lazarides, G., and Shafi, Q., Phys. Lett. B.. to be published; Georgi, H. and Wise, M.B., Phys. Lett. B., to be published; Barr, S.M., Reiss, D.B., and Zee. A., Phys. Lett. B., to be published. Dimopoulos, S., et al., Phys. Lett. B., to be published; Claudson, M., Cox, P., and Yildiz, A., Harvard preprint (1982). Preskill, J. and Wise, M.B., private communication. Adler, S., Phys. Rev. Lett. 44 (1980) 1567 and Phys. Lett. ZB(1980) 241; Zee, A., Phys. Rev. Dg (1981) 858 and Phys. Lett. B, to be published; Khuri, N., Rockefeller Univ. preprint RU 82/B130, RU 82/B131 and RU 82/B132. See talk by H.B. Nielsen in parallel session on Unified Theories. See talks by de Witt and Nicolai in parallel session on supersymmetry. Ellis, J., Gaillard, M.K., Maiani. L., and Zumino, B. in "Unification of the Fundamental Particle Interactions", ed. by Ferrara, S., et al. (Plenum Press, N.Y., 1980) p. 69. Frampton, P.H., Phys. Rev. Lett. 46 (1981) 881; Altarelli, G., Cabibbo, N., and Maiani, L., Rome preprint n. 282, 1982. H. Georgi

Discussion

N.N. KHURI .- (Rockefeller Univ). - For SU(5) the scale of symnetry breaking is 1015 GeV. But for other theories such as SO(1O) the scale of grand unification is 1017 GeV. But work on induced gravity shows that it is possible to get a rea- listic theory of gravity even if the scale of gravity is as small as (1/100). Mp~~,.,~k.I have two questions : 1) Why is ib not better and more economical to assume that the scale of grand unification is the scale of gmvitation ? 2) If that is so, how ca,z one carry out grand unification without somehow including gravity ? 14 H. GE3RGf9- I don't think that we know enough about gravity to distinguish 10 GeV from 10 GeY, since we do not have real theories which make sense at short dis- tances.

N.N. KHURI.- But I do.