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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.

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