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.