Symmetries, Supersymmetries, Strings and Spacetime: the search for a fundamental theory of physics.

The proposed research is part of a quest to find a single, complete and consistent theory of physics. While the electromagnetic, weak and strong forces have been understood since the formulation of the so-called standard model in 1967, it has so far not been possible also add the more familiar force of gravity in a consistent way. Our current description of gravity is Einstein's very successful theory of general relativity, which describes the motion of planets, stars and galaxies. At small distances the behaviour of matter and forces is governed by quantum mechanics. It is crucial for the quantum mechanical consistency of the electromagnetic and strong and weak forces that the standard model of particle physics incorporates a large amount of of symmetry. Unfortunately, Einstein's theory of general relativity is not consistent with quantum mechanics and so can not be simply combined with the standard model to provide a consistent theory of all the four forces. It is widely believed that supersymmetry, which is a symmetry that exchanges fermions (matter particles such as the electron) with bosons (force carriers such as photons of light) will play an important role in formulating a unified theory of the four forces. Supersymmetry predicts the existence of yet unknown subatomic particles, and the search for these is an important motivation behind the construction of the `Large Hadron Collider' (LHC) at CERN, a vast laboratory situated in Geneva. Strings are microscopic objects which are extended along one dimensions and can vibrate, just like strings on a violin. To date there does not exist a complete theory of strings, but the lowest energy effects of such a theory are unique as a consequence of the large amount of symmetry, and in particular supersymmetry, that they possess. These are the so-called supergravity theories. By studying these theories it has been realised that branes and a symmetry called U-duality are an important part of the full theory. Branes can similarly be thought of as microscopic generalizations of strings to objects that are extended along more than one dimension. We wish to find and understand this underlying theory of strings and branes. We propose to investigate this very intricate theory from several points of view. The first is to understand the theory at low energies, where it must produce spacetime and the four forces we know. Secondly, we will investigate the theory at very high energies, where its fundamental constituents behave like vibrating strings and branes and the notion of a smooth spacetime does no longer make sense. Our most important tool will be the enormous amount of symmetry that this theory is thought to possesses. Symmetry is a sign of underlying simplicity and beauty and has been a reliable guiding principle in reaching the understanding of physics we have today. In this process we expect to replace of our usual notion of spacetime by one which is consistent with such symmetries. This illustrates on the one hand the profound effect that a unified theory has on our understanding of nature, and on the other hand the central role played by symmetries.