Gravity and particle physics took centre stage at last year’s DESY theory workshop. As chairman of the organizing committee Dieter Lüst reports, there was plenty to talk about.

The relationship between astrophysics, cosmology and elementary particle physics is fruitful and has been constantly evolving for many years. Important puzzles in cosmology can find their natural explanation in microscopic particle physics, and a discovery in astrophysics can sometimes give new insights into the structure of fundamental interactions. The inflationary universe scenario offers a good example. Inflation is a beautiful way to understand the cosmological flatness and horizon problems (see box overleaf) and apparently induces large-scale density fluctuations consistent with experimental observations. Inflation also predicts the existence of dark matter elementary particles together with a certain amount of dark energy manifested as the cosmological constant L. This has recently become clear through fascinating new experimental results. However, some of the pieces essential for building a theory that combines the physics of the macrocosmos with all microscopic phenomena in a complete and satisfactory way are still missing.

### Quantum gravity

On the theoretical and conceptual level, the quest for a theory of quantum gravity is the most prominent and important problem facing theoretical physics. Quantizing gravity will be necessary to describe the physics at regions of very large space-time curvature – near or inside black holes, for example, or at extremely short time scales after the Big Bang. Any new theory that goes beyond the established Standard Model of particle physics and of cosmology must explain known facts in a broader and more unified perspective. At the same time it should not introduce more – and perhaps hidden – assumptions than there are facts in need of explanation. Finally, it must pass experimental tests and be verifiable (or falsifiable), at least in principle. Superstrings offer, perhaps for the first time, a promising avenue for constructing a viable theory of quantum gravity, since they contain gravity with a spin 2 graviton field as well as all the basic ingredients of the Standard Model.

The choice of topics – gravity and particle physics – for the 2001 DESY workshop (held in Hamburg) was largely influenced by impressive recent astrophysical observations showing that the overall mass and energy density of today’s universe is extremely close to its critical value (W = 1). Another main theme of the workshop was string theories, particularly the recently developed M-theory (often dubbed “the mother of all theories”) that underlies string theories. In string and M-theory, multidimensional surfaces, rather than just strings, are also allowed. These higher-dimensional membranes (or branes) and one particular type, Dirichlet, or D-branes, subject to a particular set of boundary conditions, have proved important in understanding black holes in string theory.

At DESY theory workshops, introductory lectures covering the main topics of the workshop are traditionally given on the first day. On this occasion, Costas Bachas of the Ecole Normale Supérieure in Paris presented string theory, string dualities, D-branes and M-theory. Slava Mukhanov of the Ludwig-Maximilians University in Munich discussed inflation. Stefan Theisen of the Max-Planck Institute (MPI) in Potsdam covered the holographic principle, which asserts that information contained in some region of space can be represented as a “hologram” – a theory that lives on the boundary of that region. Finally, Orsay’s Pierre Binétruy discussed the cosmological constant.

### Cosmic inflation

Cosmic inflation in the early universe is one of the most appealing hypotheses in cosmology. Inflation stretches space to be flat, and leads naturally to the density of the universe, W, having its critical value of 1. It explains the large-scale smoothness of the cosmic microwave background (CMB) and inflates quantum fluctuations from microscopic scales to the cosmological scale, thereby creating density fluctuations. In the first talk of the workshop, Paolo de Bernardis of the University of Rome, La Sapienza, showed an impressive array of new experimental CMB data from the balloon experiment BOOMERanG. These are in complete agreement with the predictions of inflation. BOOMERanG and COBE show that the universe is indeed spatially flat. Moreover, the matter-energy density, W_{M}, is clearly dominated by a large dark matter component. Most excitingly, W_{M} is not enough to flatten the universe, but there is now convincing evidence for a non-vanishing contribution W_{L} from dark energy, arising from a cosmological constant L.

One of the most burning problems is explaining the microscopic origin of the cosmological constant L, while at the same time understanding why L is so small compared with the natural scale of gravity. In this context it is very important to determine whether L is a static quantity, totally unchanged through time, or whether it is dynamic. Quintessence – a “fifth force” that changes with time – offers a concrete realization of this idea. It was introduced by Slava Mukhanov and by Heidelberg’s Christof Wetterich, who discussed how the cosmic coincidence problem (why the cosmological constant only recently started to dominate the expansion of the universe) can be explained by some kind of attractor mechanism.

Agreement between the theoretical idea of inflation and experiment is convincing. However, model building is still difficult and seems to require several assumptions and fine-tuning of parameters. This leads to the question of whether there are serious competitors for inflation, for example, in M-theory. This would be desirable since some basic arguments state that de Sitter space-times, which describe an exponentially growing universe, are difficult to implement in supergravity and superstring theories. As Fernando Quevedo of Cambridge discussed, there is a nice way to build inflationary models into brane-world models in string theory in such a way as to trigger the graceful exit from inflation. This leads to a hybrid inflationary scenario being realized in brane-world models. A more radical approach to explaining the flatness and horizon problems – one that really competes with inflation – was introduced by Burt Ovrut from the University of Pennsylvania. Taking its name from a Greek word meaning conflagration, the ekpyrotic universe theory explains the rapid expansion of the early universe as arising from the collision of branes. Through such a collision, a huge amount of energy is almost uniformly and homogeneously deposited on our universe. Despite offering a fascinating and challenging alternative to standard inflation, many aspects of the ekpyrotic universe need further investigation.

### Challenging branes and strings

A particularly compelling picture of a 10-dimensional universe has been developed over recent years. In this picture, observable gauge interactions are confined to a possibly three-dimensional domain wall, whereas the gravitational force is mediated over the entire 10-dimensional space-time. This scenario would account for the vast difference between the observed strength of the gravitational interaction and nature’s other fundamental interactions. It also offers the exciting possibility that the extra dimensions can be much larger than previously assumed – up to almost 1 mm. If the extra dimensions are compact, their sizes are constrained by high-precision experiments that measure deviations from Newtonian gravity below 1 mm, as Joshua Long of Colorado University pointed out. Depending on the coupling strength of gravity inside the extra dimensions, the present experimental upper bounds for their size vary between 1 mm and several microns. New techniques are expected to push these bounds below 1 µm. In addition, Bonn’s Hans-Peter Nilles and Valery Rubakov of Moscow’s Institute of Nuclear Research discussed more theoretical issues and exotic effects arising from extra dimensions.

One challenge in string theory is to construct brane-world models that come as close as possible to the Standard Model of elementary particles. Ralph Blumenhagen of Berlin’s Humboldt University suggested that intersecting brane worlds is a promising approach. Stable intersecting brane-world models reproducing the Standard Model can be constructed, but issues such as the correct pattern of Yukawa couplings and gauge coupling unification still need to be addressed.

D-branes have provided many important theoretical insights into the nature of gravity and gauge theory. One of the most prominent consequences of D-brane physics is that a string theory in a so-called anti-de Sitter space-time (one with constantly negative curvature) is equivalent to conformal field theories – in other words there is a deep connection between string theory and quantum field theory. This so-called AdS/CFT duality is one of the most prominent and basic consequences of D-brane physics. Further presentations on D-branes and supergravity were given by Jan Plefka of the MPI in Potsdam, Klaus Behrndt of Humboldt University, Matthias Gaberdiel and Dan Waldram of the University of London, and Thomas Mohaupt from Jena. Another important aspect of D-branes is the field of non-commutative geometry, since under general boundary conditions the world volume co-ordinates of D-branes become non-commutative. Non-commutative field theories have therefore recently received much attention, and were discussed by Luis Alvarez-Gaumé of CERN and Volker Schomerus from the MPI in Potsdam.

String theories have made great advances of late, but there remain many unsolved problems, as Hermann Nicolai of the MPI in Potsdam pointed out in his workshop summary. At a fundamental level, is there really a unified description of all string theories in terms of M-theory? It is still not clear what M-theory really is. Is it 11-dimensional supergravity together with membranes and five-branes? Or is it given by matrix theory? Or are the fundamental degrees of freedom of M-theory related to the supermembrane? The workshop could not provide the answers. Furthermore, there remains the fundamental question of how a small but positive cosmological constant L can be consistently built into superstring theory or supergravity theories. Data from future facilities will be essential in advancing our understanding of these issues.

The theoretical physics community looks forward to seeing these data, and several talks alluded to what we may expect. In astrophysics and cosmology, the study of supermassive black holes in galactic centres poses many questions on how the first black holes were formed, what masses they have, and what their final destiny is. Ralf Bender of Munich discussed these issues. Cosmology with gravitational waves could open up a new avenue for deepening our understanding of the early universe. Bernard Schutz of the MPI in Potsdam presented the status of the four ground-based interferometric gravitational wave detectors: GEO600 (Germany), VIRGO (Italy), LIGO (US) and TAMA300 (Japan). More ambitious is the LISA project, due to be launched in 2011, in which three spacecraft in orbit around the Sun will form the interferometer. LISA may even provide new information on string cosmology and brane-world scenarios. Albrecht Wagner, head of the DESY directorate, discussed future colliders, such as the LHC and TESLA, whose input is urgently needed for further theoretical progress in particle physics.

## Big Bang problems

Despite its success, there are three problems with the Big Bang model which were hotly debated at the DESY theory workshop.

***The horizon problem** Remote regions of the universe that have been out of contact – or beyond each others’ horizon – are nevertheless similar.

***The flatness problem** The universe appears to be largely “flat” – the mass-energy density W is close to its critical value of 1, which would steer the universe to a fate between a big chill and a big crunch. Big Bang cosmology predicts that any deviation from flatness in the early universe should have increased as the universe expanded, which is difficult to reconcile with observation today.

***The monopole problem** Big Bang cosmology predicts that magnetic monopoles should be commonplace, yet so far not a single one has been seen.