PROC. 19th INT. CONF. HIGH ENERGY PHYSICS TOKYO, 1978 P 9b Unification, Superunification and New Theoretical Ideas A. SALAM ICTP, Trieste ceeds as follows: §1. Introduction a) Find an internal symmetry group G, The Organizers have kindly allotted to me simple or semi-simple (with discrete symmet­ five parallel sessions—nine hours of the Con­ ries), which includes SU(2)xU(l)xSU(3)c ference—to report to the plenary session on. and whose fermionic representations describe These include sessions on 1) unification of the known (and predicted) quarks and léptons. strong, weak and electromagnetic interactions, b) Write a local theory of this internal 2) supersymmetry and supergravity, 3) quantum symmetry group G, with one coupling param­ electrodynamics, 4) formal field theory and 5) eter g and with Yang-Mills spin-one gauge new theoretical ideas. With my deepest particles. (For a semi-simple group G, dis­ apologies to those physicists whose beautiful crete symmetries can ensure that there is only work I will not be able to report, Ï have one gauge coupling constant.) The gauge reluctantly decided, in view of the shortness particles include octet of colour gluons cor­ ± of time, and the experimental interests of the responding to SU(3)C and W 9 Z° and y cor­ majority of the audience, to structure my responding to SU(2)xU(l). Assuming that report around the theme of unification ideas the gauge theory is asymptotically free, the for the four basic forces: strong, weak, elec­ unifying constant g would manifest itself at tromagnetic as well as gravitational. For low energies, through renormalization group 2 there is no question that after the unification considerations in the form as=g J47r for strong implied by SU(2)xU(l), the unification of the SU(3)C symmetry and the fine structure con­ other two forces with what may call the "elec­ stant a for the SU(2)xU(l) "electroweak" tro weak force" is likely to be one of the most force. motivating concerns in particle physics and c) The descent from G to SU(3)C on the will affect the development of the subject. colour and SU(2)xU(l) on the flavour side New theoretical ideas often take some five determines the ratio a/as in terms of the high to ten years to mature. My concern will be unifying mass M (expressed in units of a low not so much with the shortrange but rather mass ju~few GeV) in accordance with the with the long-range aspects of unification standard ideas of Georgi, Quinn and Weinberg. over a perspective of ten to twenty years ; In most of the unification models considered, in terms, if you like, of not just the LEP it is usually assumed that the unification mass and the ISABELLE accelerators, projected M is realized physically as governing the for the late 1980's but their successors of 10 masses of ultra-heavy gauge mesons. TeV centre of mass, projected for the later d) There is spontaneous symmetry break­ 1990's. The weak force will become com­ ing (SSB) which is accomplished by introduc­ parable to the electromagnetic above 100 ing a set of Higgs-Kibble spin-zero representa­ GeV. The question we shall be posing is tions of the group G, and a Higgs potential this; is the unification with the strong likely which gives rise to observed masses and other to manifest itself directly at a relatively low broken symmetry phenomena. With the energy like 10 TeV, or does it manifest itself Higgs multiplets, one introduces two sets of only at the inaccessible energy in excess of new coupling parameters: f's coupling fer­ 1012 TeV? mions and scalars and X9s describing the Higgs self-couplings. The Higgs sector is not Standard unification ideas as tightly controlled as the basic fermionic To unify weak, electromagnetic and strong, and the gauge sectors. Later we shall see the standard renormalizable gauge model pro­ that supersymmetry (Bose-Fermi symmetry) is 934 A. SALAM one way of controlling the arbitrariness of this through supersymmetry is exceedingly con­ sector. stricting. It would have been pleasing (in van e) To include gravity—a spin-2 gauge Nieuwenhuizen's phrase) if nature had "indeed theory—a compact internal symmetry G can­ been aware of our efforts". It does not not suffice. Einstein's gravity can be for­ seem to be on present evidence—or at least on mulated as the gauge theory of Weyl's SL(2,C) present evidence as we interpret it now. symmetry. This group structure must then be Perhaps we need to re-examine, ab initio, the included in the basic group together with the charge concept, questions like how many compact G. flavours, how many colours, how many quarks f) To include gravity, a radically new and and leptons, why internal symmetry and why fascinating approach has been favoured. non-Abelian internal symmetry at all? In There are many ways to describe this—and a this respect, I shall finally touch upon some of part of this talk will be concerned with these the deepest ideas reported at this Conference, diverse approaches—but one of the simplest connected with space-time topology and inter­ is to say that one brings gravity into a unified nal symmetries. Thus there will be four parts gauge scheme not just through SL(2,C)~ to this talk. 0(3, 1), but instead through the larger structure 1) The standard unification models utiliz­ Sp(4)^0(3,2), which includes and reduces ing "simple" or "semi-simple" gauge groups. to SL(2,C)^0(3, 1) after a Wigner-Innonue 2) Global supersymmetry, unification of contraction. Fermi and Bose objects into one multiplet— g) This structure Sp(4) permits of a rather the general aspects of unification through special inclusion of internal symmetries of the grading; extended supersymmetries; and their type O(JV), and the corresponding Yang-Mills possible embedding in higher dimensional particles, through the procedure of "grading". space-times; use of extended supersymmetries Grading is the adjoining of fermionic anti- to unify gravity with matter. commuting generators to Sp(4) to give what 3) Local supersymmetry ; gauging of super- are known as ortho-symplectic structures symmetry itself, leading to a theory of self- OSp(4|A0 which include Sp(4)xSOQV) "bo- interactions of Einstein's gravitation, and of sonic" generators. "Grading"—the Fermi- these with the spin 3/2 gravitinos as well as Bose supersymmetry—implies that all multi­ their supersymmetric interactions with other plets of the graded groups contain equal types of supersymmetric matter. numbers of fermionic as well as bosonic com­ 4) The search for internal symmetries within ponents. For the particular case of OSp(4|8) space-time topological ideas. (with 0(8) internal symmetry), the basic multiplet contains one graviton (spin 2), eight gravitinos (spin 3/2), twenty-eight Yang-Mills PART I (spin 1) particles, fifty-six spin 1/2 fermions and §11. The Standard Models of Strong plus seventy Higgs scalar s. There are two distinct Electro-Weak Unification via Exchanges coupling parameters, the gravitational K^=An of Spin-One Gauge Particles ^Newtonian and the Yang-Mills g. Note that it is the grading, the Fermi-Bose super- As indicated in the introduction, one starts symmetry, which makes the basic fermions with a group G (simple or semi-simple)1 (spin 1/2) come to belong to the same multiplet 1) G includes SU(2) x U(l) X SU(3)C ; as the conventional gauge particles (spin-2 2) Its fermionic representations—and pre­ graviton, plus the Yang-Mills spin one objects) ferably the fundamental—should describe together with the spin-zero Higgs particles. known and predicted quarks and leptons2; This is a radically new type of unification 3) We shall assume that the local (gauge) where it is not so much the "uni-constant" version of G spontaneously breaks into SU(2) x aspect of gauge unification which is emphasiz­ U(l) X SU(3)C with essentially one heavy mass ed but the "uni-multiplet" aspect which is scale M; all gauge bosons not contained more to the fore. within SU(2)xU(l)xSU(3)c are ultra-heavy, This ambitious superunified approach their masses being of order M. This is follow- Unification, Superunification and New Theoretical Ideas 935 ed by a second, more familiar breaking of an electro-weakly broken global SU(3)C admitt­ SU(2) x U(l) x SU(3)C, with a medium mass ing of integer-charge (vector and axial) gluons scale. and quarks. Such particles do not need Surprisingly, there are not very many absolute but only partial confinement. candidates for the unification3 models. If G To motivate partial confinement, we remark is "simple" the current choice is between that in the parton model language, the effective 4 5 6 G=SU(5) or SO(10) or E6 . For the "semi- masses of quarks and gluons (inside the known simple" case1 (with discrete left-right-colour- hadronic bags) is rather small. There is no flavour symmetries guaranteeing one basic contradiction with medium or heavy physical constant g) the only offer is masses, outside the bags for integer (or even 4 fractional) charges. G=[SU(4)] = SU(4)Z x SU(4)*|flavour The "Archimedes effect"—light quarks and xSU(4) xSU(4)*| x cololir gluons inside—and heavy outside—is well (or more generally perhaps [SU(n)]4). known in other branches of physics. (Elec­ Except for quark and lepton spectra, the trons in a metal, nucléons in shell-model "simple" groups SU(5), SO(10) and E6 offer calculations, are examples of situations where fairly similar dynamical predictions, so far as the effective masses are different from physical the high mass unification signals are con­ liberated masses.