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YEARAGO John Schwarz and Michael a problem best avoided. Since then the A Green announced a discovery that search for a unified theory has been an pointed the way toward tying up a lot of active subject of research, with today's loose ends in . With a mathematical theoretical physicists seeking a quantum breakthrough in their superstring theory, they mechanical field theory that would, at last, suddenly found themselves with a very embed Einstein's general theory of relativity promising candidate for a unified field theory comfortably in . describing all four known fundamental Not everyone has been looking for the of nature - , the weak and solution in superstrings, a word coined by strong forces, and . The search for a Schwarz. In fact, before August 1984 unified field theory has been the most com­ Schwarz, then senior research associate, and pelling problem in modem physics, whose Green, visiting associate at Caltech (from solution was Einstein's dream; it has eluded Queen Mary College, University of London), physicists 'ever since. Although electromagne­ may have been the only two people in the tism and the weak have been established world working on superstring theory. Now as being related to each other, and progress hundreds have jumped on the bandwagon. has been made toward linking up the strong Although not directly involved in the work, force, until a decade ago the inclusion of Murray Gell-Mann, Nobel laureate and the gravity appeared to most theoretical physicists Robert Andrews Millikan Professor of

19 , has been providing the - building blocks of the . encouragement along the way and considers Besides the serious drawback of missing most the recent work of extraordinary importance. of the particles, the theory also required a "If it's not the answer, it's an important step rather intimidating 26 dimensions of space­ in moving toward the answer," he says. "If time. superstring theory works, it will prove to be Fifteen years ago at Princeton, Schwarz the key to early cosmology as well as particle and Andre Neveu, with a contribution from physics." Pierre Ramond (who later also came to Cal­ In superstring theory all elementary parti­ tech), set out to get rid of these difficulties. cles are, instead of points as previously They came up with a version of the theory assumed, strings, albeit very short ones (10,33 that incorporated fermions and that led to the cm, - a Planck length), that exist in 10- elimination of the troublesome tachyons after dimensional space-time. They're not just the simple modification of consistently omit­ mathematical fictions, insists Schwarz, but ting certain parts of the theory. The number really do exist as one-dimensional curves with of dimensions of space-time was now 10 zero thickness. But they're so small that for instead of 26. But although this new string most practical purposes they are well approxi­ theory was, according to Gell-Mann, "a beau­ mated by points. The string-like structure tifully consistent theory" and "very exciting," becomes important only at extremely high quantum chromodynamics emerged at about energies (or very small distances) and could the same time (partly the result of Gell­ be directly observed, says Schwarz, only in Mann's own work and that of Harald experiments at 10 19 GeV. Current accelera­ Fritzsch, who was then also at Caltech) and tors are capable of only 103 GeV. was recognized as the correct theory of Such a bizarre picture (although Schwarz hadrons and the strong force. maintains that it's really quite conservative) was superseded as a theory of hadrons, and its didn't suddenly appear out of nowhere last popularity waned. year. The basic idea of strings, including But Schwarz stuck with string theory any­ some mathematical machinery for them, has way, convinced that, in Gell-Mann's words, been around since the late 1960s, when it was "somehow, sometime, somewhere, it would proposed as a theory of hadrons - the still be useful." Schwarz came to Caltech at numerous different subnuclear particles Gell-Mann's invitation in 1972, and in 1974 including the and , which are he and Joel Scherk hit on the idea that the held together by the strong force. But there ... key particle':"":'" of mass 0 and spin 2 - which were a few problems with the original string had been so troublesome for the theory of hadrons. For one thing, it con­ interpretation, might actually be a , tained tachyons, massless particles that travel the hypothetical particle that carries the force faster than the speed of light, whose existence of gravity. What was impossible for a theory was essentially impossible. And it did not of hadrons and the strong force was "just contain any fermions. Fermions are particles what one wants for a graviton," says Schwarz. that obey the Pauli exclusion principle, that (A graviton will not be observed directly in is, no two of them can simultaneously occupy the near future because its interactions are so the same quantum state. The basic fermions weak, but it definitely does exist, Schwarz are the leptons (which include the , says.) And Einstein's theory of gravitation the muon, the tau, and their ) and appeared as an approximation to the theory. With the revival of the string idea in a new context, their whole perspective changed. They abandoned the attempt to make it fit hadrons and began to consider string theory as a possible quantum theory of gravity - and all other phenomena as well. From this perspective the previously troublesome com­ ponents of string theory settled quite neatly into place. Scherk and Schwarz reduced the hypothesized size of strings 20 orders of mag­ nitude - from the size of the nucleus to 10,33 cm. They published papers in 1974 and 1975 reformulating Schwarz and Neveu's original string theory as a quantum theory of gravity. With the simple modification mentioned above, the reformulated string theory pos­ sessed and had (Einstein's theory of gravitation combined with supersymmetry) as an approximation. A kind of supersymmetry arose out of Schwarz, Neveu, and Ramond's first string theory in 1971, when it was still being applied to hadrons. The more commonly discussed kind of supersymmetry was introduced for point particles at about the same time by a Russian group and later independently by Wess and Zumino in Europe. It involves a mathematical transformation that inter­ changes fermions and bosons (including the laboratory in Geneva, in 1979, and thus so-called gauge particles - , , began a fruitful collaboration that has contin­ and , which shuttle between particles ued during several months of each subsequent and transmit forces), so that each fermion has year, on one side of the ocean or the other. a boson partner and vice versa. These Since supergravity had captured the attention hypothesized particles have some fanciful of most others, the two were left in peace. "It names (Schwarz claims no responsibility for was nice, really," says Green. "We could them); for example, the boson partners of work on a topic and be sure that no one else quarks and leptons are squarks and sleptons, had already done it." And their results were and the fermion partner of the is the interesting to enough people (Gell-Mann and photino. Observation of these predicted par­ Edward Witten of Princeton, in particular), ticles, which would confirm supersymmetry, that at least "no one treated us as if we were may be possible with some of the powerful crazy." new colliders now on the drawing boards, or The most popular version of supergravity even with existing ones, Schwarz believes. postulates 11 dimensions of space-time, which The search has already begun. Green says is impossible, since the correct One of the stumbling blocks of a quantum theory must be chiral, that is, left-right asym­ theory of gravity in which gravitons and other metric, or mirror asymmetric, as are the laws elementary particles are described as points is of physics. He believes that chiral theories can the occurrence of infinities. Supersymmetry exist only in an even number of space-time turns out to playa crucial role in canceling dimensions, such as the 10 dimensions of out certain infinities. Calculations in quan­ superstring theory, which Schwarz had tum mechanical theories require contribu­ already suggested in 1972. And where are the tions from all particles, the bosons in certain other six, apart from the three of space and examples giving positive contributions and one of time that we know? Presumably the fermions negative ones. When they are they're too small to be observed and are kept separate, you get the infinities that you described as curled up, collapsed, or com­ don't want, but in superstring theory the fer­ pacted into a sort of six-dimensional ball. mion and boson contributions are combined, While the nine spatial dimensions could have canceling each other out and producing finite been equivalent in the first moments of the results. This also happens to some extent in Big Bang, symmetry could break in the supergravity, although it is a point-particle rapidly cooling and expanding universe, leav­ theory, but not to an extent sufficient for ing three dimensions very large and six very meaningful finite results, according to small. Schwarz. In the late 1970s supergravity was Although chirality is an essential feature of itself a hot candidate for a unified field theory Schwarz and Green's theory, chiral fermions - so hot that Scherk and Schwarz's 1974 create what was thought to be an inescapable paper caused little stir. Very little was pub­ problem of anomalies (inconsistencies intro­ lished on strings until Schwarz and Michael duced by quantum effects). It was considered Green's first joint paper in 1981. such a generic problem in higher dimension Green got involved with strings on meet­ theories that theoretical physicists were sty­ ing Schwarz at CERN, the particle physics mied by it until the summer of 1984, when

21 Green and Schwarz showed that anomalies unified field theory looked to be within reach. could cancel in superstring theories. For Gell-Mann, one of the important Their calculations showed that there were answers superstring theory offers is to the no anomalies for superstring theory in the question of the confusing and continuing case of two specific symmetry groups - the proliferation of elementary particles. Why breakthough that suddenly attracted so much are there so many? Superstring theory sug­ attention. In particle physics symmetry gests that there are actually an infinite groups, of which there are an infinite number number of particles, with only some of them of possibilities, are used to define transforma­ lying in the low-mass states, that is, relatively tions that relate particles to one another and low; in many cases the low-mass states are thereby relate the properties of those particles. still high-mass states as far as experimental Quantum field theories that describe the fun­ physicists are concerned. "But these infinitely damental forces of nature other than gravita­ many particles all obey a single very beautiful tion (electromagnetism and the weak and master equation," says Gell- Mann. He strong forces) use specific symmetry groups to describes the theory as that of a field taken as describe the interactions and the quanta that a function of a one-dimensional path or carry them. These established and accepted string (which corresponds to an infinite theories have not used theoretical criteria to number of functions of a point) in space­ select symmetry groups but have picked them time. Just as the strings of a musical instru­ because they are the groups that fit the experi­ ment can yield an infinite number of har­ mental facts. For example, the electromag­ monics, so the theory's strings can vibrate in netic force is characterized by a group of an infinite number of modes. transformations called U(1). A symmetry The second Eg of the symmetry group group labeled SU(3) describes the strong force brings with it a bizarre phenomenon of much of quantum chromodynamics, and SU(2) the interest to astrophysicists - shadow matter, weak force. Glashow, Weinberg and Salam that is, a whole other corresponding (although received the Nobel Prize in 1979 for mixing not exactly corresponding) type of matter that the SU(2) and U(1) symmetry groups (the interacts with the matter we observe only electroweak forces). The theory that encom­ through interactions of gravitational strength passes all three symmetry groups (SU(3) x - that is, very weakly except in large aggre­ SU(2) x U(1) is called the , gates. On the basis of observable behavior of and it describes all the known forces and par­ galaxies, astrophysicists believe there must be ticles - except gravity. a great deal of unseen "dark" matter exerting Ideally, however, the symmetry group gravitational force - matter whose existence should be uniquely determined by the theory would determine whether the universe will itself without having to "dial knobs" in the forever expand or whether it will eventually equations, as Schwarz puts it. Schwarz and collapse on itself. It is intriguing to consider Green found, not by dialing any knobs but by that the Eg shadow matter, hidden from our using superstring theory, that mathematical perception, may provide the answer. consistency (that is, elimination of the anom­ The potential of superstring theory is alies) made two particular symmetry groups exciting, and, according to Green, "it may pop out - groups designated SO(32) and soon be able to explain a great deal of experi­ Es x Eg. These are both very large symmetry mental information." This potential for groups (496 generators) easily able to encom­ explaining observed phenomena has put a lot pass all known sym­ of physicists in gear, notably the group at metries. Schwarz and Green came up with a Princeton working with Witten. Mathemati­ superstring theory with the SO(32) symmetry cians are getting involved too, in particular group that was free of anomalies and attempting to describe the geometry of the six infinities, and just a few months later a group curled-up dimensions. One likely possibility of researchers from Princeton, taking off from is that they form what is called a Calabi-Yau Schwarz and Green's work, presented a super­ space, which is a type of six-dimensional string theory for Eg x Eg. This particular space of great importance in pure symmetry group is especially exciting because mathematics. it readily breaks down to the Standard Model. "We've formulated the basic equations," Eo had long been a favorite of Gell-Mann says Schwarz, who is now professor of (and others), who had been hoping someone physics. "Now all we have to do is solve would find a string theory for it. Suddenly a them." D - JD

22 ENGINEERING & SCIENCE / SEPTEMBER 1985