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.
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.