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Glimpses of superhistory

26 February 2001

Nearly 30 years after its discovery, supersymmetry remains the prime candidate to cure all of the ills of our
understanding of elementary particle behaviour. Putting aside the question of experimental evidence, a recent
meeting looked at the history of supersymmetry.

Supersymmetry is now 30 years old. The first supersymmetric field theory in four dimensions – a version of
supersymmetric quantum electrodynamics (QED) – was found by Golfand and Likhtman in 1970 and
published in 1971. At that time the use of graded algebras in the extension of the Poincaré
group
*was far outside the mainstream of high-energy physics

Three decades later, it
would not be an exaggeration to say that supersymmetry dominates high-energy physics theoretically and has
the potential to dominate experimentally as well. In fact, many people believe that it will play the same
revolutionary role in the physics of the 21st century as special and general relativity did in the physics of the
20th century.

This belief is based on the aesthetic appeal of the theory, on some indirect evidence and
on the fact that there is no theoretical alternative in sight. Since the discovery of supersymmetry, immense
theoretical effort has been invested in this field. More than 30 000 theoretical papers have been published and
we are about to enter a new stage of direct experimental searches.

The largest-scale experiments in
fundamental science are those that are being prepared now at the LHC at CERN, of which one of the primary
targets is the experimental discovery of supersymmetry.

The history of supersymmetry is exceptional.
In the past, virtually all major conceptual breakthroughs have occurred because physicists were trying to
understand some established aspect of nature. In contrast, the discovery of supersymmetry in the early 1970s
was a purely intellectual achievement, driven by the logic of theoretical development rather than by the
pressure of existing data.

Simultaneous discovery

To an extent, this remains true today. The
history of supersymmetry is unique because it was discovered practically simultaneously and independently
on the both sides of the Iron Curtain. There was very little cross-fertilization – at least in the initial stages. As
such, it is not surprising that eastern and western research arrived at this discovery from totally different
directions.

While scientific interactions could have been mutually beneficial, they did not occur. Indeed,
the political climate of the 1970s precluded such interactions. Of course, once it was recognized that
supersymmetry could be integrated into and extend the standard model of fundamental interactions, progress
on both sides of the Iron Curtain were recognized. However, it was only recently that some of the pioneers
who opened the gates to the superworld in the early 1970s met face to face for the first time – in
Minnesota.

As so often when exploring new ground, some early work on supersymmetry was hit and
miss. Golfand and Likhtman initially reported a construction of the super-Poincaré algebra and a version of
massive super-QED. The formalism contained a massive photon and photino, a charged Dirac spinor
and two charged scalars (spin-0 particles).

Likhtman found algebraic representations that could be
viewed as supersymmetric multiplets and he observed the vanishing of the vacuum energy in supersymmetric
theories. It is interesting to note that this latter work still only exists in Russian.

Subsequent to the work
of Golfand and Likhtman, contributions from the East were made by Akulov and Volkov, who in 1972 tried
to associate the massless fermion – appearing due to spontaneous supersymmetry breaking – with the
neutrino. Within a year, Volkov and Soroka gauged the super-Poincaré group, which led to elements of
supergravity. They suggested that a spin 3/2 graviton’s superpartner becomes massive on “eating” the
Goldstino that Akulov and Volkov had discussed earlier. The existence of this “super-Higgs
mechanism”
in full-blown supergravity was later established in the West.

A mathematical basis for
the work of Volkov and collaborators was provided by the 1969 paper by Berezin and Katz (published in
1970), where graded algebras were studied thoroughly. In his memoirs, Volkov also mentions the impact of
Heisenberg’s ideas on the making of Volkov-Akulov supersymmetry.

In the West, a completely
different approach was taken. A breakthrough into the superworld was made by Wess and Zumino in 1973.
This work was done independently, because western researchers knew little if anything about the work done
in the Soviet Union. The prehistory on which Wess and Zumino based their inspiration has common roots
with string theory – another pillar of modern theory – which in those days was referred to as the “dual
model”.

Around 1969, the dual-resonance model of strong interactions, found by Veneziano, was
formulated in terms of four-dimensional harmonic oscillators. Nambu advanced the idea that these oscillators
represented a relativistic string. After that the scheme was reformulated as a field theory on the string world
sheet. The theory was plagued by the fact that the spectrum contained a tachyon but no fermions and
it was consistent only in 26 dimensions. These problems motivated the search for a more realistic string
theory.

*Words in italics are explained in the superglossary, next page.

What are superparticles?

The known elementary particles come in two kinds – fermions, such as
quarks, electrons, muons, etc (matter particles), and bosons, such as photons, gluons, Ws and Zs (force
carriers). The key feature of supersymmetry is that every matter particle (quark, electron, etc) has a boson
counterpart (squark, selectron, etc) and every force carrier (photon, gluon) has a fermion counterpart
(photino, gluino, chargino, neutralino, etc). This doubling of the particle gene pool is because supersymmetry
is a quantum-mechanical enhancement of the properties and symmetries of the space-time of our everyday
experience, such as translations, rotations and relativistic transformations.

Supersymmetry introduces a
new dimension – one that is only defined quantum mechanically and does not possess classical properties,
such as continuous extent. The particle-superparticle twinning can assuage several theoretical headaches, such
as why the different forces – gravity and electromagnetism – appear to operate at such vastly different and
apparently arbitrary scales (“the Hierarchy Problem”). The extra particles provided by supersymmetry are
also natural candidates for exotica, such as the missing dark matter of the universe.

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