**by Steve Bryson**

We have learned that, according to the current 'standardmodel' of the interactions between particles, there are twoforces that are important for interparticle interaction. Theseare the strong nuclear force (described by QCD) and theElectroweak force (described by the electroweak theory). (Ateveryday energies, the electroweak force acts like two forces,the weak nuclear force and electromagnetism.) So, when gravity isincluded, there seem to be three distinct forces in nature whichare apparently independent. In addition, the standard model hasmany arbitrary numbers, such as the strength of the forces, thenumber and masses of the particles, the particular choice ofgauge symmetries (= dimensions of the quantum wave space) and soon.

It has also been observed that, due to the fact that all theelementary particle forces in nature have a strength whichdepends on the distance between the interacting particles (thefurther the separation the stronger the force in QCD and the weakforce while the further the separation the weaker the force forQED) there is a distance (about 10-28 centimeters) at which allthe forces are of equal strength. This suggests that at thatdistance the separate forces may actually be a single force.

Inspired by the unification of the electromagnetic and theweak nuclear forces into a single electroweak force, the nextquestion that is naturally asked is 'can we further unify thesethree forces into two or even one single force?' thereby reducingthe number of arbitrary parameters in the theory. The theoriesthat attempt to do this are called unified field theories. Thereare several brands of unified field theories currently in voguewhich we will consider separately.

Here is a brief description of each brand:

**Grand Unified Theories (GUTs)**: These are the first andmost modest of the unified field theories in that they onlyattempt to unify the strong and the electroweak force, ignoringgravity. They are patterned on the successful electroweak theorywithout any conceptual modifications, and were introduced in1974.

**Supersymmetric Theories** (also called supersymmetry):These theories start by postulating a new, unobserved symmetry ofinterchange between fermions and bosons. This automaticallyintroduces many new particles and forces and it was hoped that wewould discover a supersymmetric model that happened to containall the known physical forces including gravity. While there wassome hints at success in this for a while, supersymmetry itselfhas not panned out.

**Kaluza-Klein Theories**: These theories postulated theremarkable idea that spacetime has more than four dimensions. Themost popular Kaluza-Klein model postulated that spacetimeactually has 11 dimensions, 10 of space and 1 of time. Then allthe gauge symmetries of quantum field theory are understood to bemuch like the rotational symmetries of the 11-dimensionalspacetime.

**Supersymmetric String Theories** (also called superstringtheories): This theory tries to combine the best of the above,but it starts by assuming that elementary particles are reallytiny (10-30 cm) strings, and that the different particles arereally different vibrations on otherwise identical strings. Thenassume that the interactions are supersymmetric and take place ina ten dimensional (9 space and 1 time) spacetime. Discover thatin this case certain technical difficulties that were present inthe above models are absent for superstring theories. Hope(convince) that this means that superstrings are the correctapproach, and as in any supersymmetric theory there are lots ofparticles and forces to fit nature into hope that this contains acorrect description of nature. In this case the forces arederived, not put in by hand.

Now let's look at each of these cases in somewhat more detail.

These theories are based on theories that are conceptuallyidentical to the electroweak theory. The only difference is thatthe dimension of the quantum wave space is larger. It turns outthat the smallest dimension quantum wave space that fits both theelectroweak force and QCD has 5 complex (10 normal) dimensions(see gauge theories section of handout 3). Three of these complexdimensions correspond to the three colors of a quark of QCD andthe other two correspond to the electron and neutrino directions(as in the electroweak theory). This is called the minimal SU(5)theory. It relies on a spontaneous symmetry breaking mechanismmuch like the electroweak theory. It is really just a bigger copyof the electroweak theory. It predicts that there are 24 forcecarrying bosons, 8 of which are gluons, 3 the W and Z particlesof the electroweak theory, and one photon. The remaining 12particles (called X and Y particles) are supermassive (a hundredtrillion times the mass of a proton) bosons that carry the newunified force.

The predictions of the minimal SU(5) model include that a 5complex dimensional quantum wave pointing in one of the quarkcolor directions can rotate into an electron or a neutrinodirection by emitting an X or Y particle (much like the muon canrotate into a muon neutrino by emitting a W particle). This wouldcause hadrons (particles made of quarks) to decay into newhadrons and leptons. Thus a particular prediction is that theproton may decay into a pion and a positron. This is the infamousproton decay, and should take place, on the average, in about1032 years. We can observe this by getting 1032 protons in oneplace (like a tank of water) and then one proton should decay inabout a year. This has been done, but no proton decay has beenseen. While the final judgment is not in, it currently looks badfor the minimal SU(5) model.

There are other predictions of the minimal SU(5) model thatare in striking agreement with observation, including theprediction that the electrical charge of some quarks should beone third the charge of the electron. There are others, but theyare too technical to mention here.

There are many other grand unified models (using quantum wavespaces of greater than 5 complex dimensions) that may givecorrect unifications of QCD and the electroweak theories. Thedifficulty is that we have no way of determining via observationwhich of these theories may be right.

Inspired by the prevalence of gauge symmetries in quantumfield theory, some physicists have postulated that there is asymmetry between the fermion type particles and the boson typeparticles. In other words the physics should be the same if weinterchanged, for example, electrons with photons. This wouldmake the relationship between fermions and bosons much like therelationship between particles and antiparticles: the existenceof a fermion would automatically imply the existence of a boson(called the fermion's supersymmetric partner). As this isobviously not the case, these physicists say that thisfermion-boson symmetry (called supersymmetry) is 'badly broken'.Then as under this symmetry one can generate lots of theoreticalparticles and forces, one hopes that by simply assumingsupersymmetry one can explain all the known particles and forces.

The original motivation for postulating supersymmetry are manyfold. They include: the rather metaphysical idea that"nature likes symmetry and would not pass up an opportunitylike this"; the hope that known bosons would turn out to bethe supersymmetric rotations of known fermions, thus cutting thenumber of fundamental particles in half; also some technicalmotivations involved in the fact that at least one type ofsupersymmetric theory is completely finite (thus not requiringbig bad renormalization theory); Supersymmetry automaticallypredicts a force that acts like gravity (this has been referredto as supergravity). There are some other more technicalmotivations.

The current status of supersymmetry is: none of the knownbosons can be partners of any of the known fermions, thuspredicting twice as many particles as are currently known--inother words this motivation backfired; one (out of eight) type ofsupersymmetric theory (known as N=4 supersymmetry) has beensolved exactly (by Stanley Mandelstam) making it the only quantumfield theory ever to be exactly solved but it turned out not tocontain the real world; Other types of supersymmetry may not becompletely finite after all.

It is now generally felt that supersymmetry by itself is notthe answer.

These theories take the ideas of supersymmetry and postulatethe spacetime is bigger than we thought. They postulate thatspacetime actually has more than 4 dimensions. The most popularmodel gives spacetime 11 dimensions (not to be confused withquantum wave space dimensions), 10 of space and 1 of time. Thenthe reason that the universe looks 4 dimensional (three space andone time) is that the other 7 space dimensions are rolled up verytightly into little circles. These circles are so small that (toquote Prof. Mary Galliard) "when you go in those sevendirections you get back where you started so quickly that younever realize that you went anywhere" so that you nevernotice those seven dimensions.

The motivation for postulating those seven extra dimensions isthat quantum field theory in general and supersymmetry inparticular are better behaved in these 11 dimensional spacetimesthan in 4 dimensions. Also, it is hoped that the gauge symmetriesof the quantum wave functions could be understood as somethinglike rotational symmetries in the 11 dimensional space.

While Kaluza-Klein theories made for some interesting modelswith very interesting mathematics, no new physics came out ofthem.

(These theories are not to be confused with something called'cosmic strings' which are something else entirely.)

The basic postulate of superstring theories is that elementaryparticles are really very short (10-30 cm) strings which wiggle.The different observed particles are different wiggles inotherwise identical strings. When supersymmetry is included inthe description of the strings, one discovers that one candescribe just about any particle that one wishes. Further, thesuperstring theory is very well behaved on a technical level ifthe universe is really 10 dimensional (9 space and 1 time), wheresix of the space dimensions are rolled up into very tiny circlesmuch like in the Kaluza-Klein theories. String theoriesnecessarily contain forces that behave just like gravity, andthey may give a quantum description of gravity that is completelyfinite.

It turns out that if you phrase your theory just right youfind that there are only two (very large) possible gaugesymmetries allowed, and both of them contain the observedsymmetries of QCD and the electroweak theory. Thus in some senseyou have actually derived the existence of QCD and theelectroweak theory from the idea of strings. There are alsopredicted many forces that have not yet been observed as well asmany as yet unseen particles. One possible prediction is thatthere is a whole set of particles just like the observed particlein nature except that they do not interact in any way (exceptperhaps gravitationally) with the observed particles. This is theso-called 'shadow matter' that may solve certain problems inastronomy.

From 1983, when the first major technical successes weredemonstrated, until about 1990 superstrings have been the voguein the physics community. Lately, however, many physicists havebecome disenchanted with string theory. In any case, superstringtheory is far from mature enough to make any actual quantitativepredictions that can be tested by experiment.

I think it is fair to say that there is quite a lot of turmoiland uncertainty of direction in the theoretical particle physicscommunity. One of the main problems is that the standard model,with all of the uncertainties and arbitrary structures that itcontains, accurately accounts for just about every majorobservation in particle physics. For technical reasons, however,we can expect something new at the very next generation ofparticle accelerators currently coming on line at Fermilab inIllinois, SLAC in Palo Alto, and CERN in France/Switzerland. Weeagerly await the result from these new accelerators.