Supergravi t y and Superstrings

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1 Supergravi t y and Superstrings MURRAY GELL-MANN Physics Department California Institute of Technology Pasadena, California Over the last decade, theorists have been searching hard for a unified quantum field theory of physical interactions with or without gravitation. The standard SU, x SU, x U, theory has three independent coupling constants and numerous dimensionless parameters determining the mass ratios, the weak coupling matrix, etc. The number of sets of Higgs bosons and the representation to which they belong appear arbitrary. The theory cries out to be embedded in a bigger and more nearly unified theory. The fact that the coupling constants appear to come together somewhere between 10 GeV and the Planck mass of - 2 x loi9 GeV suggests a unified Yang-Mills theory, for example with SU5 and three fermion families (fermions in 5 + n). However, such a theory, with one coupling constant, still has numerous dimensionless parameters and arbitrary Higgs boson behavior. Renormalizability is assured, but the constants, although they absorb all the infinities, are not calculable and the unified Yang-Mills theory is still obviously incomplete. In particular, the very small and rather similar ratios of AQcD/MuNIF, various MFERMlON f MUNlF, and M1N,,osoNs/M Np must be explained. Of course, AQcD/MuNIF is related to exp - const/ffun,f, but then the value of the unified coupling constant near the unification mass needs explanation, which is like a modern version of the old problem of calculating 1/13,, Although there is as yet no direct evidence, an attractive modification involves switching to N = 1 super-yang-mills theory, in which spin 1 bosons are accompanied by new spin y2 gluinos, photinos, etc., spin y2 fermions are accompanied by new spin zero squarks and sleptons, and spin zero higgsons are accompanied by new spin /2 shiggsons! The super-yang-mills theory is more easily compatible with experiments on proton decay, and besides, it may provide the only way to keep some Higgs boson(s) light. We may note here that there is a set of theories finite at least to two loops, including just one of phenomenological interest, with SU, as the gauge group, three quarkand higgsons-shiggsons as follows: one 23, squark, lepton-slepton families of 2 + n, four z s, four 3 s. The theory has a number of parameters and can fit all experimental evidence to date. (The extra higgsons, mostly heavy, might be useful for producing enough baryons in the early universe.) While N = 1 supergravity, generalizing Einstein s gravity theory, is not necessarily very divergent itself (first divergences setting in perhaps at three loops), it is terribly divergent when coupled to external N = 1 supermatter, such as N = 1 super- Yang-Mills theory with N = 1 supermultiplets of spin /z and spin zero. Such N = 1 supermatter coupled to N - 1 supergravity with a cutoff has been used to show how important modifications are introduced by supergravity coupling into such quantities as the proton decay rate and branching ratios; however, such a divergent theory really does not make sense. We still require a finite, parameter-free theory and one that unifies all of physics, including Einsteinian gravitation. Three paths are being explored in the search for the ultimate unified theory of 325

2 326 ANNALS NEW YORK ACADEMY OF SCIENCES physics. The first path involves N > 1 supergravity in four dimensions, without external supermatter, particularly the largest such theory, N = 8 supergravity, where there is no room for external supermatter. The N = 8 supergravity supermultiplet itself contains all the haplons (fundamental fields of the theory). N = 8 Supergravity Haplons: gravi ton gravitinos vector bosons spin /2 fermions spin 0 bosons spin i/2 fermions vector bosons gravitinos graviton Jz / y Here, divergences probably do not set in until we get to three or perhaps seven loops, but there is no known reason to exclude them. N = 8 supergravity has Newton s constant, K, and may also have a dimensionless self-coupling parameter, e, for the gauge group, SO8, with 28 generators. Unfortunately, SOs does not contain SU, x SU2 x U,. Moreover, the list of spin 12 particles, while long enough, does not quite match the list of quarks and leptons we know. If N = 8 supergravity is to match experience, then the elementary particles we know cannot be the haplons of the theory, but must be composites and/or solitons. The second and third paths involve higher-dimensional theories, with ten or eleven dimensions, where six or seven, respectively, are supposed to roll themselves up spontaneously into a small structure that is not observable directly, but which is detected only through its effects on the spectrum and symmetries of the elementary particles and on very early cosmology. Higher-dimensional theories that have been studied are either superstring theories in ten dimensions or else N = 1 or N = 2 supergravity theories in eleven and ten dimensions, respectively. The latter are much more recent and, I believe, much less interesting, but they have received much more attention. If we perform trivial dimensional reductions (just circles for all the curled-up coordinates), then we obtain the relations: - 3/2-2 N=l,D=ll supergravity, 1 N = 2A, D = 10 N = 2B, D = 10 supergravity supergravity (non-chiral) / (chiral) N = 8, D = 4 supergravity supergravity (non-chiral)

3 CELL-MANN SUPERGRAVITY AND SUPERSTRINGS 327 Ten-dimensional supergravity theories (N = 1, N = 2A, and N = 2B) are all very singular, even for one loop. Eleven-dimensional supergravity theory is trivially nondivergent in one loop because it is odd-dimensional, but in two loops it also must be highly divergent. Nevertheless, many brilliant theorists have spent a great deal of time on these theories, concentrating especially on generalizing the old Kaluza-Klein idea of getting electromagnetism from a fifth dimension. Here, they use six or seven extra dimensions (index, i), our usual four dimensions (index, p), and components, g,,, of the metric tensor to construct gauge vector potentials, where the gauge symmetries are isornetries of the six- or seven-dimensional space. While a trivial dimensional reduction (just a product of seven circles) turns N = 1 supergravity in eleven dimensions into N = 8 supergravity in four dimensions (with 28 vector bosons that can gauge SO,), we notice that SO8 does not include SU, x SU, x U, and remark that a different, nontrivial dimensional reduction could lead, for example, to Kaluza-Klein bosons gauging SU3 x SU, x U,. However, this Kaluza-Klein program of accounting for gauge bosons is flawed. For one thing, it is very difficult, and perhaps impossible, to obtain a chiral theory with massless gauge bosons after dimensional reduction. For another, the dimensional reduction over a space with nontrivial isometries tends to give a huge cosmological constant at the classical level. In any case, the higher-dimensional supergravity theories are no doubt hopelessly divergent. The cosmological constant is proportional to the vacuum expected value of the energy density. Supersymmetry makes it vanish in the simplest theories, where there is no spontaneous violation. In realistic theories, where supersymmetry is gauged and spontaneously violated, it is by no means obvious how to get rid of the cosmological constant. Yet the effective cosmological constant in astronomy is less than times the natural unit involving the Planck mass. If the cosmological constant gets a large value at the classical level, then (1) we can try to cancel that against quantum corrections, hoping to do it convincingly to avoid introducing the biggest fudge factor in history, or (2) we can try to exploit (with Hawking) the possibility of quantum gravity giving a foaminess to space-time, thus disconnecting the theoretical cosmological constant from the astronomical one. Another promising strategy, however, is to have the cosmological constant vanish classically and then try to make the corrections vanish too. The former is possible if we abandon Kaluza-Klein, but the latter may be harder. The third path, as mentioned above, involves superstrings. A superstring theory has an infinite number of fundamental boson and fermion states, of all spins, initially (as coupling starts from zero) stable and lying on an infinite number of straight Regge trajectories, so that the states with spins increasing by two at a time are spaced equally in mass squared. The spacing is related to the string tension. The coupling introduces level widths and modifies the trajectories. String theories may be thought of as embodying the bootstrap principle; in a sense, the infinitely many particles of the theory are bound to one another by means of forces coming from the exchange of the same particles, which then form bound states that are again the same particles. Although string theories can be written in terms of quantum fields that are functions of a one-dimensional string rather than a point, they are still local theories because when an interaction causes a string to divide into two strings, for example, the new ones just correspond to dividing the old one at a point.

4 328 ANNALS NEW YORK ACADEMY OF SCIENCES Superstring theory was originally invented in 1971 by Neveu and Schwarz in an effort to describe hadrons. Unlike earlier string models, it incorporated not only a boson spectrum, but also a fermion spectrum proposed by Ramond. The theory seems to require ten dimensions; of course, one hopes that six dimensions curl up spontaneously. In 1971, the theory possessed a kind of supersymmetry, which was noted by Gervais and Sakita. In 1976, Gliozzi, Scherk, and Olive noticed that the theory could be improved by the consistent omission of certain pieces, after which one could show that there were no ghosts or tachyons. The theory could then be shown to possess regular N = 1 supersymmetry in ten dimensions and to contain N = 1 supergravity in ten dimensions as a sector of the theory. This was after the invention of space-time supersymmetry and supergravity, which, if they had not been invented in other ways, could have been discovered in superstrings. Meanwhile, QCD had given a presumably correct description of hadrons, with strings only an approximation. Thus, around 1974, Scherk and Schwarz suggested that the string theory be used as a unified theory of all physics, generalizing Einsteinian gravitation, with the trajectory slopes changed from - l/(cev) to /(GeV)2. Original (Type I) superstring theory has closed strings, generalizing supergravity, and open strings, generalizing super-yang-mills. It is known how to construct a formal superstring theory when the gauge group is classical (i.e., unitary, orthogonal, or symplectic); simple arguments then eliminate the unitary groups. At first, the choice of orthogonal or symplectic group seems arbitrary, but recently that has been found to be untrue. Among the three constants, Newton s K, string tension, T, and super-yang-mills coupling constant, y. there is one obvious relation and now another has been shown to exist. Thus, the theory is parameter-free apart from MPlonck. As in any parameter-free theory, all the small quantities we know about must be calculable and must somehow come out small, in a way that depends on the nature of the spontaneous dimensional reduction and of the low-mass sector that results. The initially massless states of the open strings in Type I superstring theory belong to the adjoint representation of the gauge group. The states of the first excited level (initially around the Planck mass) belong to a different representation. The states continue to alternate between the two representations (i.e., for the orthogonal and symplectic groups, which are known to give formal superstring theories). Type I superstring theory reduces, on truncation to the initially massless sector, to N = 1 supergravity in ten dimensions, coupled to N = 1 super-yang-mills in ten dimensions with the gauge group of the superstring theory, plus some interesting extra terms discussed later. The truncated theory is terribly divergent, of course, but shows the character of the superstring theory. Extraction of results of superstring theory is crucially dependent on the nature of the spontaneous dimensional reduction. Trivial reduction of Type I theory (ten dimensions reduced to four dimensions and the product of six circles) gives N = 4 supergravity coupled to N = 4 super-yang-mills as the initially massless sector. N = 4 Supergravity Four Dimensions: Jz 1 graviton 4 gravitinos /2

5 CELL-MA": SUPERGRAVITY AND SUPERSTRINGS vector bosons +I 4 spin '/2 fermions + '/2 I+ 1 spin 0 bosons 0 4 spin '/2 fermions - y2 6 vector bosons -1 4 gravitinos - yz 1 graviton -2 N = 4 Super-Yang-Mills Four Dimensions: J* 1 vector boson +1 4 spin '/z fermions + '/2 6 spin 0 bosons 0 4 spin y2 fermions -y2 1 vector boson -1 All in adjoint ' representation of the gauge group Breaking this last down to N = 1 supersymmetry, we obtain: 1 Super-Yang-Mills x Adjoint - y2-1 3 N = 1 Matter Supermultiplets :(? ] x - yz Adjoint A more complicated dimensional reduction will give different results and can break down the gauge group. During the last couple of years, Michael Green and John Schwarz have found that there are two more ten-dimensional superstring theories, IIA and IIB, with only closed strings. They reduce, on truncation to the initially massless sector, to N = 2A and N = 2B supergravity, respectively, in ten dimensions. However, the superstring theories are finite to one loop instead of divergent like the corresponding supergravities. In addition, we see that IIA and IIB superstrings, when truncated to the initially massless sector and trivially reduced to four dimensions, yield N = 8 supergravity. All three superstring theories, although they have the traditional description as "S-matrix" theories on the mass shell, can also be written as field theories (with fields as functionals of strings, instead of functions of points) with local couplings. So far, the field description is not covariant. In the present description, there are just polynomial couplings like:

6 330 ANNALS NEW YORK ACAriEMY OF SCIENCES (Basic super-yang-mills coupling) or for open strings (Basic self-coupling of supergravity) for closed strings Higher couplings like fourth degree terms in Yang-Mills theory come from summing over exchanges of heavy intermediate excited states. Type I and Type IIB superstring theories and N = 2B supergravity in ten dimensions appear at first to be threatened by the possible existence of anomalies (gravitational, Yang-Mills, and mixed) that would destroy gauge invariance and unitarity, as well as finiteness or renormalizability. (The last applies to strings since ten-dimensional supergravity is divergent anyway.) IIA superstring theory, being non-chiral, has all anomalies vanishing trivially and is finite to one loop. However, it is less interesting than IIB for comparison with observation, just because it is non-chiral. Last year, Witten and Alvarez-Gaumi were surprised to discover that all anomalies mysteriously cancel for N = IIB ten-dimensional supergravity. That same result could be demonstrated for the IIB superstring. That made IIB theory, which is also finite to one loop, an attractive candidate for the universal theory. Type I, with its arbitrary gauge group, seemed less attractive. In the last few months, however, Green and Schwarz have shown that all of the anomalies of Type I string theory with a classical gauge group vanish to one loop if and only if the gauge group is SO(32) and also that the theory is finite rather than renormalizable to one loop if and only if the gauge group is SO(32). Here, therefore, we have a very impressive form of unification with (super)-gravitational closed strings and (super)-yang-mills open strings implying each other and controlling each other s behavior. The string theories, IIA and IIB, as well as Type I with SO(32) as gauge group, are all finite to one loop and all anomaly-free. They seem increasingly desirable in this order since Type IIA is non-chiral, while Type IIB lacks gauge bosons other than Kaluza-Klein ones, which give problems with chirality on reduction to four dimensions. There is one more gauge group, the nonclassical (exceptional) group, E, x E,, that can yield finiteness and freedom from anomalies, provided a superstring theory can be built on it. I shall go into more detail below about that exciting prospect. The finiteness of string theories in one loop is of a kind that strongly suggests the

7 GELL-MA : SUPERGRAVITY AND SUPERSTRINGS 331 possibility of finiteness persisting to all orders, unlike the finiteness in one loop of N = 1, D = 11 supergravity, which appears to be merely a trivial consequence of D being odd and unlikely to persist in higher order. Also, the demonstration of the persistent absence of anomalies to all orders in string theory would really require this finiteness. Where would the gauge bosons come in according to the different kinds of proposed unified theory? N = 8, D = 4 supergravity: At least some would be composites or solitons. N = 1, D = 1 I supergravity: Kaluza-Klein. Type I superstring, D = 10: Haplons that survive nontrivial dimensional reduction. Type IIB superstring, D = 10: Again, composites or solitons. (This last according to Gell-Mann and Zwiebach, who showed how in this theory two dimensions seem to want to roll up into a teardrop with a U, isometry, where the Kaluza-Klein boson acquires a mass and is useless as a gauge boson.) It is presumably possible to integrate out all the initially massive states of a superstring theory and obtain a very complicated effective theory of the initially massless sector, which is not divergent if superstring theory finite. Expanding that effective theory at low energies for Type I superstring with S0(32), we obtain first the truncated theory with N = 1 supergravity and N = 1 super-yang-mills theory in ten dimensions, with a correction term that breaks supersymmetry, but cancels anomalies, and then other terms that restore supersymmetry and so forth. The sum of these terms should give back the exact superstring theory with initially massive states integrated out. It may be that this kind of summation always leads to a superstring. Witten also has shown that freedom from anomalies in ten dimensions for Type I superstrings implies freedom from anomalies in four dimensions. Kaluza-Klein aficionados want many isometries for their extra six- or sevendimensional space in order to get massless gauge bosons. Type I superstring fans want as few as possible: The field equations may require R,/ = 0 (for the extra dimensions), where R,, is the Ricci-Einstein tensor. (There can still be, though, some Riemann- Christoffel curvature, R,,, -f 0.) The condition of R,/ = 0 (extra dimensions) will give no cosmological constant at the classical level and also no nontrivial isometries leading to extra massless gauge bosons. Even trivial U, isometries leading to massless Kaluza-Klein vector bosons may be eliminated by the requirement of surviving mass1ess spin l/z fermions. Then there would be no Kaluza-Klein bosons at all. Note that in the dimensional reduction of a Type I superstring, if (Rlk,,) # 0, then the background Yang-Mills field strength, (Gf) f 0 (as in the presence of a generalized monopole). Spatial and Yang-Mills symmetries are violated together by related amounts. Now there are many unanswered questions about superstring theories and their dimensional reduction; I shall briefly mention just a few. If the field equations allow many possible dimensional reductions, which one wins? Of course, to discuss quantum cosmology, we must adopt the many-worlds approach to quantum mechanics, which is a good idea anyway. Then, do we, following Hawking, transform to a Euclidean space, with e - e?, and minimize the quantum-corrected

8 332 ANNALS NEW YORK ACADEMY OF SCIENCES action, S, so that by an inverse probability argument we have the most probable universe? Maybe the mathematics saves us the trouble and allows only one dimensional reduction. What about sizes of extra dimensions? If we are using Kaluza-Klein ideas, then we are limited by the fact that the coupling parameters, e, are of order RP,~nck/Rextmd,menr,~nr for the Kaluza-Klein gauge bosons and these e s would be too tiny if the Rexf,odrmenr,ons were much larger than RPlonek. With Type I superstrings, we do not have this limitation. What are then the restrictions on Rexf,omme,,slonr from observation? Could we even have some of them very much larger than the Planck length? In superstring theories (Type I or II), the closed strings generalize supergravity, which generalizes Einsteinian gravitation, and the superstrings must obey a generalization of general relativity. Here, therefore, we have the reverse of Einstein s situation: theory first, principle afterward. What is the principle? It must be one of great importance. Now let us return to the possible gauge group, Ex x Ex. If there is a Type I string theory based on E, x E8 (which has dimension 496 and rank 16 like SO(32)), it also would give freedom from anomalies and finiteness to one loop. Theorists have been investigating whether there is some mathematical trick that makes possible a Type I E8 x Ex superstring. (We recall that existing methods permit only the classical orthogonal and symplectic groups, of which only SO(32) is allowed by anomaly considerations.) It is clear that E8 x E, is highly desirable as the gauge group of a superstring: (1) With all initially massless spin 1, 1/2, and 0 particles in the adjoint representation of the gauge group, it is very suitable to have a group with only one pair of that serve, in a sense, low-dimensional representations, (1, 248) and (248, A), as adjoint, fundamental, and spinor all at the same time. (2) The adjoint representation, (1, 248) and (248, I), contains a natural color, SU, (that of the non-complex-number part of the underlying octonions, as pointed out by Giirsey), and the right kind of tlavor variables (if there is a suitable reduction of symmetry) to describe the spin 1, I,$, and 0 particles we know and love. Very recently, a new type of superstring theory in ten dimensions has been found by Gross, Harvey, Martinec, and Rohm. They call it a heterotic superstring theory, but 1 shall refer to it as Type III/II. It can be thought of as a hybrid of the Type I superstring in ten dimensions and the old Veneziano string in 26 dimensions; alternatively, the extra 16 coordinates can be treated as fermionic or else we can introduce internal degrees of freedom attached to a ten-dimensional superstring. Although it is a theory of closed strings only, it does involve an internal super- Yang-Mills gauge group in ten dimensions. That gauge group can only be SO(32) or E, x E,. The initially zero-mass sector of the Type III/II theory is the same as that of the Type I theory (for S0(32), and also for Es x Es if a Type I theory exists for that group), but the representations to which the higher-mass states belong are completely different. For S0(32), the next states above the super-yang-mills particles in the adjoint representation 496 belong to the representations 1 and 527 in Type I theory and

9 CELL-MA : SUPERGRAVITY AND SUPERSTRINGS 333 the higher states oscillate between these and the adjoint. In Type III/lI theory, what lies above the adjoint 496 is a dimensional reducible representation, where = Here, is the four-index antisymmetric tensor in 32 dimensions and is a spinor. The higher-mass states belong to larger and larger reducible representations. For Ex x Ex, the picture in Type III/II theory is similar and even the dimensions of the reducible representations are the same as for SO(32). In this case, we have 496 = (1,248) + (248,L); = (1,L) + (1,1> + (1,248) + (248,1) + (248,228) + (38_75,1) + (1, 3815); and so forth. In each case, the sequence of representations 496, 69252, etc., together with a fictitious singlet, form an irreducible representation of the Kac-Moody algebra, [a,,, a,] = & z a,+,,k + md,, d,+,,*, where m and n run over all the integers (positive, negative, and zero) and i and j run over the 496 generators of the group, SO(32), or E, x Ex. The Type III/II superstring, regarded as a ten-dimensional theory, is no exception to the statement made earlier that Kaluza-Klein bosons are unnecessary and probably unwanted; however, if we do introduce sixteen extra commuting dimensions and then shrink them to zero in order to describe the E, x E, gauge symmetry, then a kind of formal Kaluza-Klein procedure is involved at that stage. That may well be the only form in which the Kaluza-Klein idea survives. Some work has already been done on the possible reduction of gauge symmetry in an E, x E, superstring theory (Type III/II or, if it exists, Type I) as ten dimensions are reduced to four. Candelas, Horowitz, Strominger, and Witten have studied such reductions over a certain kind of Ricci-flat (R,, = 0) six-dimensional space. Several of these Calabi-Yau spaces are known and more are being discovered. Candelas et al. have found at least one of considerable phenomenological interest. For the solution found in that space, the background field strength is like an SU, monopole and breaks down one of the Ex s to E,. (We note that E, includes E, x SU, and that for this embedding, E, is the group of transformations commuting with SU,.) The occurrence of SU, in this connection seems to be the necessary and sufficient condition for an N = 1 supersymmetry to survive the dimensional reduction. In this example, what survives below the Planck mass is a unified super-yang-mills theory with gauge group, E,, and four families of spin /z and spin 0 particles, each in a 22 of E,. Of course, E6 is an elegant generalization of SU,, and the 22 is a of SU,. There is also a super-higgs phenomenon involving generalization of the 5 + a nonlinear representation of E, such that the Higgs bosons are effectively in the adjoint representation 73. The symmetry is thus broken to something like SU, x SU, x u, x u, x u,. The remaining E, is unbroken and describes a kind of shadow world of particles coupled to known particles only through interactions of gravitational strength (including some processes involving virtual excitations of states above the Planck mass). We must check carefully what would be the consequences for cosmology. It looks as if the truly unified quantum field theory of all particles and interactions may be at hand, but a great deal of work is needed on dimensional reduction and extraction of low-energy results and cosmological implications before a real comparison with experience is possible.

10 334 ANNALS NEW YORK ACADEMY OF SCIENCES DISCUSSION OF THE PAPER M. BLOCK (Northwestern University, Evanston, IL): What is the relation of this theory to proton decay? M. GELL-MANN (California Institute of Technology, Pasadena, CA): The E, super-yang-mills theory presumably gives a rate of proton decay in the same range as that given by other supertheories. As usual, the coupling to supergravity introduces some uncertainty in practice because we do not yet know how to compute that coupling without a cutoff. V. VUILLEMIN (CERN, Geneva, Switzerland ): From the superstring theory, do you expect more generations of quarks and leptons? GELL-MA : I can answer with a firm Maybe. A. WHITE (Argonne National Laboratory, Chicago, IL): On the issue of the underlying principle, why should a theory of the universe be formulated on the light-cone? Alternatively, why should there not be a fundamental theory of surfaces rather than strings? CELL-MA : Whether the superstring theories, written as quantum field theories of strings, can be formulated in a manifestly covariant manner is a purely technical matter as long as the theory is really covariant, which it is. As to surfaces or other still more complicated structures, no one has ever shown that they can compete with superstrings in furnishing a consistent, perturbatively finite, perfectly bootstrapped theory of the world that contains supergravity and super-yang-mills theory. G. L. KANE (University of Michigan, Ann Arbor, MI): Do you think the fermions that come out of this theory at the Planck scale will be the same as those we see (quarks and leptons) at low energies? GELL-MANN: The simplest situation would be for the dimensional reduction to lead to a unified super-yang-mills theory with families of spin /2 and spin 0 particles, all initially at zero mass, with a mechanism for spontaneous mass generation that leaves some of the particles very light; those would be the ones we can detect at accelerator energies. KANE: It seems one should be leery of forcing the spectrum of elementary fermions to look like the familiar quarks and leptons. Quarks and leptons may be composite after all. GELL-MA : An alternative possibility is certainly for the fundamental theory to lead to a system of relatively low-mass entities that are not known particles, but rather constituents out of which the known particles are built as composites or solitons. S. MESHKOV (National Bureau of Standards, Washington, D.C.): What is the SU, contained in the breakdown, En 3 SU, x Eg? GELL-MA : Physical SU, groups, including SU, of color, would have to come out of E,. The SU, group about which you are asking is just the one that occurs in E, 3 SU, x E6 in such a way that the adjoint 2$8 of En becomes (8,i) -I- (1,7_8) + (3, 22) + (3, Zi). -. In the theory, the background En field strength transforms like an SU, monopole and that is the SU, we are discussing.

11 GELL-MANN SUPERGRAVITY AND SUPERSTRINGS 335 KANE: If the particles we know (quarks, leptons, gauge bosons, and their supersymmetric partners) go in a 248, what other particles can we expect since ours do not fill up 248? GELL-MANN: The resulting super-yang-mills theory with spin /2 and 0 superfamilies need not fit into a 248. As we mentioned, one reduction gives E6 for the former and four 2J s for the latter. Note that dimensional and symmetry reduction take place together. Of course, the adjoint and 27 of E, do involve new particles. D. SCHRAMM (University of Chicago, Chicago, ZL): Is the shadow E8 identical in structure to our E8? Such a symmetry would cause a problem cosmologically since it would result in too many low-mass particles. GELL-MA : No. It appears that the shadow E8 may be unbroken, which would produce even more low-mass (or zero-mass) particles. If that is really the case, then we must make sure that the fact that these particles are coupled to ours only through interactions of gravitational strength (or weaker) is sufficient to prevent a clash with experience.