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Atomic and molecular

Atomic and molecular

Supersymmetry makes its case

01 Sep 2000

Supersymmetry: Unveiling the Ultimate Laws of Nature
Gordon Kane
2000 Perseus Books 224pp £15.95/$26.00hb

On the right track?

In 1951 Herman Weyl, a pioneer in the application of the mathematics of symmetry to physics, published a popular account of the field. His book was called, quite simply, Symmetry. To the uninitiated, Gordon Kane’s new book Supersymmetry might be construed as evidence that the world of physics has been gripped by the same inflationary trend that has turned fashion models into “supermodels”. However, neither the topic nor the terminology is new.

Supersymmetry arose from the discovery in the early 1970s that certain quantum field theories exhibit a symmetry between the “Fermi fields” associated with matter and the “Bose fields” associated with forces. This symmetry was considered so surprising that it deserved a new name.

But why the surprise? Quantum field theory naturally incorporates the wave-particle duality of quantum mechanics. It might be thought that this should remove the distinction between particles of matter and waves of radiation, but it really just turns it into a distinction between Fermi and Bose fields. Fermi fields are associated with particles called fermions that obey an “exclusion” principle. This essentially prevents them from “condensing” and is an obvious requirement for the construction of any solid object. Bose fields, on the other hand, are not so restricted, and their associated particles – bosons – actually prefer to condense into a single quantum state, the photons in a laser beam providing an example.

Fermion physics is radically different from boson physics. But if nature is supersymmetric, then this difference must be just an illusion! Prior to 1970 this not only seemed physically impossible but was also, apparently, forbidden by the mathematics of symmetry. The physicists who first realized that it was, after all, possible, were thus founding a new branch of mathematics. But is nature supersymmetric? We don’t yet know for sure, although we soon may do, and Kane’s book is an attempt to provide the scientifically literate layperson with the perspective needed to understand the import of such a discovery.

Supersymmetry predicts that for every known fundamental fermion particle there exists an (as yet undetected) fundamental boson particle, and vice versa. So, for example, the electron (a fermion) is paired with a hypothetical “selectron” (a boson), while the photon (a boson) is paired with a hypothetical “photino” (a fermion). These hypothetical “superpartners” must be massive enough to have escaped detection so far, but Kane’s belief, which is shared by many, is that at least some will be discovered within the decade by high-energy experiments at large laboratories such as CERN and Fermilab.

The term “high energy” also refers to the theoretical effort that goes in to understanding the results of these experiments, although you might not guess this from a perusal of the “theory” section of the Los Alamos high-energy physics archives, which is dominated by articles on superstrings and M-theory, often in space-times of dimensions other than four. Much of this work is also concerned with the implications of supersymmetry, but the focus is on the basic principles underlying phenomena such as quark “confinement” and black- hole “evaporation”, with little attempt to confront experimental findings. You are more likely to find a discussion of recent high-energy experiments in the “phenomenology” section of the archives.

Indeed, Kane himself is a “phenomenologist” and his book concentrates on the immediate implications of supersymmetry, should convincing evidence for it be discovered in experiments at the facilities that are currently being built. One chapter provides an overview of the experimental situation with a useful table of current and planned collider facilities.

Experiments to date have largely confirmed the Standard Model of elementary particles and their electroweak and strong interactions. The techniques needed to deduce the consequences of this theory for the purpose of comparison with experiment were worked out in the 1970s, and the two physicists who were mainly responsible for this – Gerard ‘t Hooft and Martinus Veltman – were awarded last year’s Nobel Prize for Physics. Nevertheless, few believe that the Standard Model is complete. Apart from recent experimental results that have shown the need for some modification of the Standard Model, the main worry for theorists is that the (still hypothetical) Higgs particle, which is crucial to the success of the model, creates an incoherent instability, known as the “hierarchy problem”.

Kane does a good job of explaining how supersymmetry helps here, and how it improves the prospects for unifying the electroweak and strong forces. He makes the point that supersymmetry was not invented to solve these problems – unlike other ad hoc proposals, which typically solve one problem at the cost of making others more intractable. Contrast this, so Kane urges, with supersymmetry: once introduced to solve a problem in one area it provides potential solutions to problems in others. Kane provides an excellent bullet-point summary of the problems that supersymmetry could solve.

An example of this fecundity of supersymmetry is expounded in a chapter entitled “What is the universe made of”. Astronomers assure us that most of the universe must be made of unknown and invisible “dark matter”, the most likely candidate for which is a stable massive particle that has so far escaped detection. This is, in itself, further evidence that the Standard Model is incomplete, but the main point is that supersymmetry naturally provides a candidate for this particle in the form of the LSP, or “lightest super- partner”. Kane overstates the case here because one needs an additional symmetry, other than supersymmetry, to ensure the stability of the LSP.

Of course, in a book of this kind many details must be left out in the interests of readability, and Kane is to be congratulated for having written a very readable book. I would have to temper my recommendation with a caution that it should be read as a case made for a cause, rather than as an objective account, but I recommend it nonetheless. Kane does an excellent job of marshalling his evidence. It is a pity that we didn’t have this book years ago when, according to one of Kane’s anecdotes, research into supersymmetry was blocked in the UK by an unsympathetic establishment.

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