Edward Witten

Our prehistoric ancestors did notneed any modern equipment todetect the effects of what we now

call the electromagnetic interactions. Lightis pretty obvious in everyday life, and otherelectromagnetic effects, such as static electricity, lightning bolts and the magneticproperties of some rocks, such as lodestone,were well known in ancient days.

But it takes quite a bit of modern technol-ogy to discover even the existence of the weakinteractions — let alone to understand them.We first became aware of weak interactionswith the discovery of radioactivity in 1896.Some radioactive nuclei decay by emitting‘b-particles’, which we now understand asenergetic electrons. Such nuclear b-decay isthe most accessible window into the weakinteractions, and was the only one availableuntil the middle of the last century, whencosmic ray detectors, nuclear reactors andparticle accelerators arrived on the scene.

Electricity, magnetism and light onceseemed to be three different topics. Their unified understanding, obtained in the nine-teenth century, led scientists to describe themcollectively as ‘electromagnetic’phenomena.

Electromagnetism seems a good dealmore obvious than the weak interactions.But in our modern understanding, which is based on something called the ‘standardmodel’ of particle physics, the two are perfectly in parallel. For example, electro-magnetism is described by Maxwell’s equations, and the weak interactions aredescribed by a quite similar, albeit nonlinear,set of equations (called the Yang–Mills equations). To give another example, an elementary particle called the photon is thebasic quantum unit of electromagnetism,and similar particles called W and Z bosonsare the basic quantum units of weak interactions. Because of this close relation-ship between electromagnetic and weakinteractions, modern particle physicists refer to them collectively as the ‘electroweak’interactions.

If weak interactions are so similar to electromagnetism, why do they appear sodifferent in everyday life? According to thestandard model, the key is ‘symmetry break-ing’. Even if the laws of nature have a symme-try — in this case, the symmetry betweenelectromagnetism and weak interactions, orbetween the photon and the W and Z bosons— the solutions of the equations may lackthat symmetry.

For example,in a liquid,an atom is equallylikely to move in any direction in space —there are no preferred coordinate axes. But ifwe cool the liquid until it freezes, a crystal will form, which has distinguished axes. Alldirections in space are equally possible ascrystal axes,but when the liquid freezes,somedistinguished axes will always emerge. Thesymmetry between the different directions inspace has been lost or ‘spontaneously broken’.

Similarly, according to the standardmodel, just after the ‘Big Bang’ there was aperfect symmetry between the photon andthe W and Z bosons. At the high tempera-tures that then existed, electromagnetismand the weak interactions were equally obvi-ous.But as the Universe cooled, it underwenta phase transition, somewhat analogous tothe freezing of a liquid, in which the symme-try was ‘spontaneously broken’. The W and Zbosons gained masses, limiting the weakinteractions to nuclear distances and puttingtheir effects out of reach of the unaided eye.The photon remained massless, as a result ofwhich electromagnetic effects can propagateover human-scale distances (and beyond)and are obvious in everyday life.

Most aspects of the standard model havebeen abundantly tested by experiment. Forinstance, the magnetic moment of the electron is measured down to the twelfth significant figure, with results that are inbeautiful agreement with theory. Many pre-dicted properties of the W and Z bosons havebeen verified to three or four digits. Mostrecently, the mechanism by which the stan-dard model violates the symmetry betweenmatter and antimatter has been tested in laboratories in California and Japan.

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The one facet of the standard model thatwe have not yet been able to test experimen-tally is perhaps the most basic: how is thesymmetry broken? However,we have a prettyclear idea of where such information can befound. Just as one can use atomic masses andbinding energies to estimate the meltingpoints of crystals, one can use the W and Zmasses and other observed properties ofelementary particles to estimate the hightemperature or energy that particle accelera-tors need to achieve to explore electroweak-symmetry breaking. According to these estimates, electroweak-symmetry breakingmay be in reach of the world’s most powerfulaccelerator, the Tevatron at Fermilab inChicago, and should certainly be in reach ofthe Large Hadron Collider (LHC), the newaccelerator that is projected to go online in2007 at CERN, the European particle-physics laboratory near Geneva.

What do we expect to find? In the original(and textbook) version of the standardmodel, the key to electroweak-symmetrybreaking is an entity called the Higgs particle.At high temperatures, Higgs particles, likeother particles, move at random. But as theUniverse cools, Higgs particles combine intoa ‘Bose condensate’,an ordered state in whichmany particles share the same quantumwave function, leading — in the case ofhelium — to superfluidity. The electroweaksymmetry is broken by the ‘direction’ of theBose condensate (in an abstract space thatdescribes the different particle forces) inroughly the same way that in a crystal, therotational symmetry is broken by the direc-tions of the crystal axes. Although this proposal is simple and fits the known facts,

When symmetry breaks downElectroweak-symmetry breaking: solving the riddle of how symmetry isbroken may determine the future direction of particle physics.

Spoiling the spin: when the ball rolls down the slope, it will break the symmetry of the hat.

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it is unlikely to be the whole story. A seem-ingly artificial adjustment of parameters isneeded to make the Higgs particle mass smallenough for the model to work.

Numerous proposed alternatives solve thisparticular problem, although they introducepuzzles of their own. One idea, motivated by a phenomenon that occurs in superconduc-tors, is that the Higgs particle arises as a boundstate. This would solve the problem of gettingits mass right, but also requires a host ofnew particles and forces, which have not yetbeen observed. They should be detectable at the LHC. So far, models of this type have run into a great deal of difficulty, but maybenature knows tricks that human modelbuilders do not.

A more radical idea is ‘supersymmetry’, anew symmetry structure of elementary particles in which quantum variables areincorporated in the structure of space-time.The new symmetry prevents the particleinteractions that would make the Higgs particle mass too big but, again, predicts ahost of additional new particles that mightbe discovered at the LHC, and perhaps at the Tevatron.

Supersymmetry is one idea about electroweak-symmetry breaking that has hadreally convincing successes.A relation betweendifferent particle interaction rates based onsupersymmetry is well confirmed experi-mentally. Moreover, our most interesting

attempts at a more complete unification ofthe forces of nature (‘grand unified theories’and ‘string theory’) really only work if super-symmetry is assumed. On the other hand,supersymmetric models raise numerousperplexing questions to which human modelbuilders do not yet have convincing answers.If supersymmetry is confirmed, then learn-ing how nature dealt with those questionswill probably give us crucial clues about adeeper understanding of nature.

Other ideas about electroweak-symmetrybreaking go even further afield. One line of thought links this problem to extradimensions of space-time, subnuclear insize, but observable at accelerators. Thisapproach is probably a long shot, but thepay-off would be huge — discovering extradimensions could give us the chance fordirect experimental tests of the quantumnature of gravity and black holes.

Finally, another line of thought links electroweak-symmetry breaking to the darkenergy of the Universe, which astronomershave discovered in the past few years byobserving that the expansion of the Universeis accelerating. From this point of view, onetries to relate the relative smallness of theHiggs particle mass to the smallness ofthe dark energy. One approach is theanthropic principle, according to which thedark energy and the Higgs particle mass takedifferent values in different parts of the

Universe,and we inevitably live in a region inwhich they are small enough to make lifepossible. If so, many other properties of theUniverse that we usually consider funda-mental — such as the mass and charge of theelectron — are probably also environmentalaccidents. Although I hope that this line ofthought is not correct, it will inevitablybecome more popular if experiment showsthat electroweak-symmetry breaking is governed by the textbook standard modelwith a Higgs particle and nothing else.

As yet,none of these theoretical proposalsabout electroweak-symmetry breaking are entirely satisfying. Hopefully, by the end of this decade, experimental findings at the Tevatron and the LHC will set us on the right track. But the diversity and scope of ideas on electroweak-symmetrybreaking suggests that the solution to thisriddle will determine the future direction of particle physics. ■

Edward Witten is at the Institute for AdvancedStudy, School of Natural Sciences, Princeton,New Jersey 08540, USA.

FURTHER READINGGunion, J. F. et al. The Higgs Hunter’s Guide (PerseusBooks, New York, 1990). Kane, G. Supersymmetry: Unveiling The Ultimate LawsOf Nature (Perseus Books, New York, 2001).Peskin, M. Beyond The Standard Model online athttp://arxiv.org/abs/hep-ph/9705479

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