Fundamental interactions are the basis of our description of Nature, including the origin of the Universe. While the end of the 19^th century saw the unification of electricity and magnetism, resulting in the theory of special relativity, it took until the last quarter of the 20^th century to extend this picture to weak and, to a large extent, strong interactions. Although the unification of quantum mechanics and special relativity by Dirac led to fundamental discoveries, such as the existence of antimatter, general relativity still largely eludes this unification with other fundamental forces. Yet, far reaching questions, like the birth of the Universe and the generation of the current unbalance between matter and antimatter can be addressed in the existing framework, which is validated by incredibly precise predictions (like the electron magnetic moment, measured to better than one part in a hundred billion and found in agreement with theory).

Where to go next?
We will consider mainly two theoretical approaches, keeping in mind that their experimental verification may at any moment bring a new twist to the expected developments. We will also insist on the essential interplay between theory (interpretation scheme) and experiment in the preparation of new searches and in the interpretation of data.

- A first direction is the unification of gravity (general relativity) with other fundamental forces. Here we know that the context of renormalisable gauge theories proves insufficient, and extensions are needed. The currently accepted approach uses extended objects (strings) instead of point particles, the latter being associated with the lowest modes of the strings. Consistency of such theories implies the existence of extra spatial dimensions, usually only accessible at the Planck scale, i.e. 1019 GeV (some current approaches suggest instead that large extra dimensions could be reachable at current and future accelerators, we will deal with them in a separate package). Recently the M theory, now in full swing, provided a synthesis of all string approaches with deep results in quantum gravity. Central was the discovery of D-branes, which opened the way to large extra dimensions models. Here clearly, like in general relativity itself, the guide is the symmetry appeal of theories, and the mathematical consistency of the description.

This already puts interesting, although for the moment relatively general constraints on the resulting low-energy limit of the theory.

For instance, supersymmetry seems to be an important ingredient, although the scale at which it sets up is not predicted.

Important constraints are also related to the cosmological constant, a subject deeply related to the structure of the vacuum. While astrophysics and cosmology are the ideal testing grounds of some of these ideas, some general predictions of this fundamental approach, like the possible low-energy onset of supersymmetry, or the manifestation of extra dimensions, might be directly observable at accelerators. (see work packages below)

- For the time being however this fundamental approach does not provide a unique compelling model of interactions at accelerator-reachable energies. The alternative approach thus consists in starting from the non-gravitational interactions, and in studying their unification, in close relation with experiment. In particular the still incomplete unification of strong and electroweak forces may either lead to larger gauge groups at intermediate energies, or stem from complex compactification schemes. Current attention focuses in particular on the mode of symmetry breaking, the physical way in which the Brout-Englert-Higgs mechanism may be realized. Strong connections between this approach and the first exist however.

The role of theory, often important in the past, for instance in the prediction of antimatter, has become more and more critical in the large collider experiments currently operating or planned. The possibility of a "chance" discovery, of something completely unexpected certainly subsists, yet by and large, experiments must rely heavily on theoretical considerations not only for the interpretation of the data, but also at an early planning stage. The problem indeed rests in the very high rate of interactions we are facing at current machines. Despite progress in electronics, largely driven by the field itself, and cutting-edge technology, the amount of data generated largely exceeds the fast storage capabilities. A choice of events to be recorded must thus be made very quickly, often by dedicated electronics (trigger stage). Although some "unbiased" events are always recorded to check their conformity to predictions, the choice of "interesting" events (as few as one in one million) rests on theoretical models. It is simply no longer possible, at least in an accelerator set-up, to devise an experiment, and wait for what shows up! There is also no way to re-examine the rejected events.

It is the task of the theorist and experimentalist working together to extract from theoretical possibilities the critical signals used to guide the triggering and later the analysis. This requires a good knowledge of experimental possibilities, but also of the theoretical state of the art, to be able to distinguish between the idiosyncrasies of a peculiar model, and the general signatures of a class of theories (for instance, the missing momentum expected in many supersymmetric interactions).

For this, it is not sufficient to have "theorists speak to experimentalists", but each side must be able to use, to some extent, the tools of the other. In this project, special care will be devoted to such pre- and post-doctoral formation of scientists through dedicated formation programs (summer schools).

It should be stressed however that collaboration between theorists and experimentalists appears usually more in respective acknowledgements than in common publication, the reason being simply the structure of experimental groups, involving hundreds of scientists working over several years, and for which the list of authors leaves no room to include shorter term theory partners. The interplay is however essential in promoting a motor role for our experimentalist groups in their own collaborations, and must be seen as a long-haul investment.

Existing cross-disciplinary and bi-university seminars (like the existing ones on extra dimensions and on neutrino physics) will be expanded to the whole network. Annual workshops between theorists and experimentalists, organised with the help of our European partners are also part of the program.

We want also to make it clear that the primary purpose of the present proposal is not to build detector equiment, for which separate funding is secured. Instead we want to develop the existing analysis activities and capabilities of our teams, through the extra research strength of postdoctoral researchers, wich will benefit here from both experimental and theoretical support.

We now discuss the general organisation of the work, distributed into multidisciplinary workpackages. We start by outlining those packages, their detail will be presented at the end of this section.

The work packages are articulated around important physics questions and goals, their realisation implies skills from different specialists met in this network.

All centre on a better understanding of the nature of fundamental interactions, either in a "top-down" (deductive or axiomatic) or "bottom-up" (inductive, based on existing experimental or observational data, sometimes involving the set-up of new experimental analysis) approach.

These approaches are of course not completely independent, and we will point out below the complementarities between the various tasks.

While the gauge theory ideas are essential both in the present unified description of particle interactions (the Standard Model) and in general relativity, it has been so far impossible to unify the two. The currently accepted path in this direction consists in a formulation in terms of extended, rather than point-like objects, either strings or membranes, usually in high-dimensional spaces, to which the concept of supersymmetry is usually added (unification of fermions and bosons).

This approach is essentially a "top-down" one, relying on the appeal of symmetries for choosing a scheme, and the main problem is now to find how it reduces (breaks down to-) our less symmetrical world. In principle, the scales at which either the presence of extra dimensions, or of supersymmetry appear, are not fixed. There is however great reason to suppose that at least the supersymmetric scale should be within reach of our currently built accelerators, the search for supersymmetry is thus an important step in the experimental validation of these schemes. This approach also has a strong connection to the issue of CP violation and the origin of mass, which will be evoked under "Physics goal B" as string theories per se tend to be CP-conserving, and CP violation can thus be a guide to the breaking mechanisms.

Therefore ambitious theories based on large (or curved) extra dimensions, and potentially bringing back the unification scale between gravity and Standard Model forces to the TeV range, can be investigated at accelerators (limits from LEP and HERA already exist), and through neutrino disappearance mechanisms.