# Bookshelf

18 April 2000

The Quantum Theory of Fields III: Supersymmetry by
Steven Weinberg, Cambridge University Press, ISBN 0 521
66000 9 (hbk £32.50/$49.95). The third volume in Steven Weinberg’s very successful collection on “The Quantum Theory of Fields” covers the topical area of supersymmetry and appears three years after the celebrated opening ones on “Foundations”(1995) and “Modern applications” (1996). If these two volumes were considered masterpieces in a modern and original presentation of the basics of quantum field theory and its penetration in the recent development of particle physics, with the machinery of spontaneously broken gauge theories, the new volume embraces the wide subject of supersymmetry in Weinberg’s typical style, which always means a self-contained treatment of the subject, from its foundations and motivations, to its most recent application as a possible scenario for new physics beyond the Standard Model (SM). Weinberg’s main motivation for “Supersymmetry”as a quest for a unified theory relies on the possible solution of the so-called hierarchy problem, that is, the explanation of the “mystery” of the enormous ratio between the electroweak scale (around 300 GeV) and the Planck scale (1019GeV). It is worth noticing that such a fine-tuning problem, which calls for new physics at the TeV scale and is one of the main reasons for future searches at the LHC under construction at CERN, was raised by Weinberg himself in a famous paper with Eldad Gildener (1976 Phys. Rev.D13, 3333), and by two more of the main contributors to the modern theory of electroweak and strong interactions, Martinus Veltman (1981 Acta Phys. Polon. B12 437) and Luciano Maiani (1979 Proc. Summer School of Gif-sur-Yvette IN2P3 1). Supersymmetry is the only known example of the enlargement of the space-time symmetry of physical laws (the so-called Poincaré symmetry based on Einstein’s special relativity), which is consistent with all axioms of relativistic quantum field theory. In so doing it unites particles of different spin, thus predicting a variety of new species when applied to the SM of the electroweak and strong interactions. Weinberg’s exposition (in chapters 24-32) starts with a synthetic but complete presentation of the mathematical foundations of supersymmetry, called “graded Lie algebras”, which is a generalization of the concept, more familiar to physicists, of Lie algebras and continuous Lie groups (chapter 25). As a preliminary to the above, he recalls in chapter 24, with an original presentation, the “no-go” theorems, which are the basis of the (failed) attempts, prior to supersymmetry, to unite space-time with internal symmetries (such as isospin or SU(3) eightfold-way symmetries). He then undertakes, in chapter 26, supersymmetric field theories, using superfields, that is fields living in superspace, an abstract space that unifies space-time points with anticommuting coordinates, able to encompass multiplets of particles with different statistics and spin. In chapter 27, he develops the subject of supersymmetric gauge theories, which realize the remarkable marriage between the principle of local Yang-Mills symmetry with supersymmetry. The way in which Weinberg exposes the subject, with all of its subtleties and technical details, is spectacular. He covers non-renormalization theorems, supersymmetry breaking and extended supersymmetry with an original, clear and self-contained presentation. He then develops, in chapter 28, supersymmetric versions of the SM, covering most of the problems at the core of today’s search for supersymmetry in particle physics, namely the scale of supersymmetry breaking, the minimal supersymmetric SM, possible baryon- and lepton-number violation and gauge-mediated supersymmetry breaking. In the last four chapters, Weinberg develops more theoretical aspects of supersymmetric field theories, which are, however, tremendously important to the theoretical motivation of supersymmetry and its role in the formulation of quantum theories of gravity. General aspects of supersymmetry beyond perturbation theory are touched on in chapter 29, with the modern developments of electric-magnetic duality. The latter allows us to give “exact results” for the low-energy action of certain supersymmetric field theories that exhibit a Coulomb phase for the Higgs field (the Seiberg-Witten solutions). The following chapters are devoted to Feynman rules for supersymmetric field theories (chapter 30), an elegant presentation of supergravity theory (chapter 31) and its essential aspects, from the weak-field limit to local supersymmetry to all orders and the basic role of the gauge field predicted by supergravity, the spin-3/2 gravitino, in gravity-mediated supersymmetry-breaking scenarios. The final chapter is devoted to supersymmetry in high space-time dimensions and the merging role of extended objects, called p-branes, in the description of modern gauge theories as coming from more general schemes such as higher-dimensional supergravities, M-theory and string theory. The book also contains, at the end of each chapter, “problems” for the reader to exercise in the subject, even giving alternative proofs of derived results. In this respect the book, like the two preceding volumes, is well suited to graduate students in physics and applied mathematics as well as researchers who want to get acquainted with the fascinating subject of supersymmetry. The author has achieved in a superb way the important task of producing a volume on supersymmetry, building a bridge between a formal development and its most important applications in particle physics, through a self-contained and very original sequence of subjects and topics. To conclude this review, let us recall some indirect experimental signals, alluded to also in different parts of Weinberg’s book, indicating that supersymmetry is a plausible scenario for new physics beyond the SM: * the non-observation of proton decay via a neutral pion and a positron, excluding a minimal Grand Unified Theory (GUT); * the LEP precision measurements, incompatible with gauge-coupling unification for conventional minimal GUTs, but in reasonable agreement with minimal supersymmetric GUTs, with supersymmetry broken at the TeV scale; * the large top Yukawa coupling, unusually large compared with all other quark and lepton couplings; * the possible solution of the dark-matter problem with some of the natural supersymmetric particles (the neutralinos) as natural dark-matter candidates (WIMPs). Although none of these facts is per se a compelling reason for supersymmetry and alternative explanations may be found, it is fair to say that they can all be interpreted in the context of a supersymmetric extension of the SM. Whatever the final theory for quantum gravity may be, supersymmetry remains a deep and non-trivial extension of our concept of space-time symmetries. Sergio Ferrara, CERN. Lucifer’s Legacy: the Meaning of Asymmetry by Frank Close, Oxford University Press, ISBN 0 19 850380 6. Communicating science is difficult. In contrast with other fields, it needs long experience before being able to contribute. While creativity in science or the arts is often left to younger people with open minds, when it comes to explaining new developments to a wide audience, the science communicator first has to master the science itself, its teaching and its popular dissemination. Frank Close, who has already provided several popular science standards, has all it requires. Here he takes us on a tour of modern science, following a theme, the study of which started early in 19th century: the fascination and appeal of the underlying symmetry of nature, and its attendant asymmetry. The tour begins and ends in Paris, in a French garden where almost perfect symmetry appears slightly broken, that day, by a damaged statue of Lucifer. With this metaphor of our entire world, accidentally asymmetric but governed by apparently symmetric laws, Close embarks on a journey through the history of the quest to understand where the asymmetry of the universe comes from. This governs even our own existence: matter overcoming antimatter was a necessary step for there to be anything at all. Moreover, life on Earth, seen through the basic structure of organic molecules, is asymmetric. The mystery of life cannot be understood by physics alone, yet asymmetry is a property of life itself, and this thread continues throughout the book. First the author reviews symmetry at large, with examples taken from everyday life, featuring common notions and clichés. One of the enigmas dealt with is my own favourite, Martin Gardner’s puzzle: why does a mirror invert left and right, but not top and bottom? Here the author adds much of his own insight and wit (“the muscles which close a mouth are stronger than those which open it – as is well known to all who have sat in committees”). The result is a fascinating panorama, down to the molecular level, of the asymmetries around us, which have first to be discovered before being explained. The remainder of the book covers the history of the tools needed to explore matter and to reveal its hidden asymmetries. Following the pioneer work of Biot (polarization of light) and Pasteur (study of racemic acid), the end of the 19th century brought major discoveries by scientists investigating the true nature of electricity, continuing the route taken by Faraday and Maxwell. First came the discovery of X-rays by Roentgen, a key tool for decoding DNA structure half a century later. Immediately after X-rays came the discovery of the electron by Thomson, and then of radioactivity (Becquerel and the Curies) and the nucleus (Rutherford). The major cornerstones of modern physics were revealed during those few “magic” years, and they are narrated by Close in a way that reveals the hesitations and inspirations of the actors, the banal errors of those who “could have found” (Lenard, Crookes) but were not quite ready, and the genius of those who made sure that they were in the right place at the right time with the right ideas. What better plea could there be for fundamental research? All of this leads to modern physics, exploiting the concept of symmetry in a profound way, revealing hitherto unsuspected laws through delicate symmetry breaking. We are introduced to unification schemes based on symmetries broken at our energy scale, but revealed in high-energy experiments. Close explains this in detail and with amusing anecdotes, and how it guided physicists during their major discoveries of the secrets of the matter, right up to the next foreseen step – the quest to find the Higgs boson. The instrumentation and apparatus required for this quest are impressive. The incredible effort of a worldwide community at CERN for the LHC and its giant experiments help the reader to become familiar with this ultimate search for the origin of mass. On the way, the chapter on antimatter deserves admiration: antimatter is one of the most difficult notions scientists have to explain. I remember a colleague beginning a public talk by unapologetically defining antimatter as “the negative energy solution to Dirac’s equations”. What is exact is not always clear, and Frank Close takes the time to introduce antimatter, to draw its human side through Dirac’s character and by noting the time it took, from Dirac’s work in 1928 to Anderson’s discovery of the positron in 1932. The violation of “mirror” P symmetry by the weak force, how this was discovered, the violation of CP symmetry and recent evidence for the violation of time symmetry are all clearly explained, illustrated by analogies with Escher prints to help the mind see patterns in abstract spaces. We then understand that the universe, once fully symmetric, exhibited asymmetries when freezing, which enabled life to be. Life, intrinsically related to asymmetries, is the theme of this book, and Close revisits what has already been written on this theme, offering us an absorbing and scientifically correct account of symmetry and its deep implications. Yves Sacquin, Saclay. Cosmology: the Science of the Universe by Edward Harrison, Cambridge University Press, ISBN 0 521 66148 X (£32.50/$54.95).

A great deal has
happened to our understanding of the universe in the almost 20
years since the first edition of “Cosmology” became a bestseller.
Now Prof. Harrison has produced this updated and extended
second edition. It has many new sections and revisions and it is
wonderfully informative and authoritative on an amazingly
wide range of topics.

My own particular favourites are
his treatment of Special Relativity – just the way particle
physicists like it – and his explanation of Olbers’ paradox – the
clearest I’ve ever seen. The entire book is quirky and
entertaining, peppered with historical facts, extremely
perceptive questions, and provocative and challenging issues for
discussion. All of this comes with essentially no mathematics in
a very satisfactory and readable introductory overview of
modern cosmology.
Steve Reucroft, Northeastern
University.