For all its spectacular experimental successes, the Standard Model (SM) fails to give us solutions to such basic problems as why there are three copies (generations) of quarks and leptons, why there are three different gauge forces (the strong, weak and electromagnetic, with differing strengths), and how gravity should be included in a consistent quantum theory along with the gauge forces.

Supersymmetry (SUSY) is the leading contender for physics beyond the SM. Although SUSY has been around for some time and has so far had no direct experimental support, indirect experimental hints and progress in understanding the theoretical possibilities allowed for in a SUSY world have led to a new feeling of excitement. With these new ideas on the market, the Supersymmetry 2000 (SUSY2K) conference, held recently at CERN, attracted a large crowd and showed how the new SUSY ideas can help.

SUSY makes precise predictions for the quantum numbers and selection rules for many new particles. What is much more difficult is predicting the masses of these additional supersymmetric particles. The reason for this is that SUSY must be a so-called "broken" or hidden symmetry, and the mechanism of communication of SUSY breaking to the SM and its superpartners is inevitably indirect, not well constrained, and is poorly understood.

As a comparison, the unification of weak and electromagnetic gauge forces in the electroweak sector is also "broken" or hidden - with the Higgs mechanism leading to very different masses for the electromagnetic photon and the W and Z carriers of the weak force.

For SUSY, such a direct coupling to the sector that breaks SUSY (analogous to the direct coupling of the electroweak force to the Higgs) is not possible, because such a coupling leads to sum rules for the masses of the unobserved superpartners (see box) that are definitively excluded. Thus an indirect communication of SUSY breaking must be employed.

### Mass communication

Many attractive new communication mechanisms for SUSY breaking were reviewed at the SUSY2K conference. In "archetypal" SUSY breaking, gravity takes on the role of communicating between the SUSY breaking sector and the conventional world, and, until recently, this gravity-mediated SUSY breaking was considered as the most plausible possibility.

However, during the last few years many innovative new mechanisms have been proposed - "gauge mediation" (with heavy messenger particles communicating the breaking), "anomaly mediation" (via symmetries that are broken at the quantum but not at the classical level), and "gaugino mediation" (when the SUSY partners of the SM gauge bosons take on the mediating role).

These different mechanisms have characteristic mass spectra and experimental signatures. Supersymmetry might not manifest itself as neutrino-like invisible events detectable only through "missing" energy, but in several other ways, for example in events producing additional photons or stable charged particles, or models with supersymmetric particles that are nearly degenerate in mass. Experiments at LEP and elsewhere have been looking for these various possibilities, but without any luck so far (see "Particles and sparticles" below).

### Particles and sparticles

Standard Model (SM) particles come off the shelf in two kinds - fermions (matter particles) such as quarks, electrons, muons, etc.) and bosons (force carriers) such as photons, gluons, Ws and Zs. A feature of SUSY is that every matter particle (quark, electron...) has a boson counterpart (squark, selectron...) and every force carrier (photon, gluon) has a fermion counterpart (photino, gluino, chargino, neutralino...).

This doubling of the spectrum is due to the fact that SUSY is a quantum-mechanical enhancement of the properties and symmetries of the space-time of our everyday experience - such as translations, rotations and Lorentz boosts.

SUSY introduces a new form of dimension - one that is only defined quantum mechanically, and does not possess the classical properties we associate with a new dimension, such as continuous "extent".

The doubling of the particle population can fix several of the problems afflicting today's SM, for instance why the different forces - gravity, electromagnetism, weak and strong - appear to operate at such vastly different and apparently arbitrary scales (the "hierarchy problem"). The extra particles provided by SUSY are also natural candidates for exotica such as the missing "dark matter" of the universe.

### Problem solving

One of the theoretical motivations for these new models is the "flavour problem", namely that of understanding the relations between the different generations of particles. Experiments observe many approximate flavour symmetries in today's non-SUSY SM; however, these symmetries are usually violated in typical gravity-mediated SUSY breaking schemes.

Another motivation for some of the new communication ideas (anomaly and gaugino mediation) has been provided by new ideas for physics beyond the SM, such as extra dimensions beyond those accessible to us (see March p7) and multidimensional "branes" (see Superstrings, black holes and gauge theories; April 1999).

Many new ideas have also been stimulated by the exact non-perturbative results that have allowed theorists to construct explicit models of SUSY breaking, and motivated attempts to merge SUSY breaking with the visible particles. One approach involves composite (sub-quark) models, where some of the SM states are composites of a strongly interacting sector.

### Extra dimensions - are we the scum of the universe?

A natural focus of the workshop was extradimensional models, in which the world we experience is complemented by extra (but to us invisible) spatial dimensions. These models have the common feature that our SM world is realized as localized degrees of freedom living on a generalized 3-spatial-dimensional membrane ("3-brane") embedded in a universe possessing a larger number of dimensions.

In this approach, it is possible that
the fundamental scale of gravity might be the TeV scale, rather than the embarrassingly
distant Planck scale (10^{19} GeV), potentially eliminating the hierarchy problem
(see "Particles and sparticles").

This requires a fundamental rethinking of cosmology and the high-energy behaviour of SM physics. Many questions are being reformulated in terms of the geometry of the extra dimensions - their sizes and shapes, and the fields localized on them. In the same way that general relativity introduced geometry as the natural explanation of gravity, so concepts of geometry and locality replace the ideas of symmetry usually used in field theory.

Superstring theory naturally incorporates such branes and gives, at least in toy models, explicit realizations of the brane-world idea. One major question is the radiative stability of such models - that their predictions are compatible with accompanying virtual quantum effects.

Without SUSY, the apparently haphazard hierarchy of the different forces of nature, with each force having very different associated mass scales, is not stable (or rather requires fine tuning). SUSY can take care of this problem, and new light may be cast by brane physics.

At the moment there are two main approaches to the construction of extra-dimensional models. Originally, it was thought that the geometry of the extra coordinates should be distinct from our space - the universe at large could be viewed as the product of two spaces. In this case, a solution to the hierarchy problem requires large extra dimensions and quantum gravity physics at the TeV scale.

In a more recent approach, highly-curved geometries have been proposed, which
tightly constrain the brane in which we live. In this very different geometry, gravity is
concentrated away from our world, explaining its observed weakness for us. Both schemes
have very specific signatures for experiments at high-energy colliders.

Future collider experiments are also gearing up to look for new particles. The Fermilab Tevatron will resume the sparticle and Higgs searches after LEP is retired, and has quite good prospects. In the longer run, the LHC is expected to produce Higgs bosons and any supersymmetric particles. It will also be able to probe for extra dimensions at shorter scales than any previous experiments. There is optimism that the next generation of collider experiments will break out of the SM straitjacket.

The issue of the cosmological constant - the energy density of free space - has been the most striking problem in quantum field theory for many years. Experimentally, it has long been known that it is very close to zero. According to the latest observations a (very) small non-zero value is now preferred, and this is further supported by cosmic microwave background observations by the BOOMERANG and MAXIMA collaborations.

However, the result of theoretical calculations in quantum field theory is naturally a number at least 60 orders of magnitude bigger. SUSY has long held out the promise of a resolution to this dilemma, but so far has not been able to claim a solution. However, many new ideas of how to approach this problem are also suggested by brane theories and were discussed at SUSY2K.

### Dark matter

If SUSY is correct then it would have played an important role in the Big Bang. For example, SUSY might have played a role in the generation of the observed matter in the universe. However, one of the most important issues is that of possible SUSY remnants of the Big Bang, which could play the role of the invisible "dark matter" known to pervade our universe. One of the most attractive features of SUSY is that it provides quite naturally a candidate, the "neutralino". Experimental searches for such particle dark matter are just beginning to reach the range suggested by theory. However, SUSY must also contend with the strong upper limits on various unwanted supersymmetric particles such as gravitinos.

SUSY2K showed that supersymmetry is assured of an exciting future.