Symmetry, supersymmetry, strings, branes and gauge theories; physics from the Planck to the QCD scale.

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The proposed research is part of a quest to find a single, completeand consistent theory of physics. While the electromagnetic, weakand strong forces have been understood since the formulation of thestandard model in 1967, it has so far not been possibleto add the more familiar force of gravity in a consistent way. Ourcurrent description of gravity is Einstein's very successful theoryof general relativity, which describes the motion of planets, starsand galaxies. At small distances the behaviour of matter and forces is governedby quantum mechanics. It is crucial for the quantum mechanicalconsistency of the electromagnetic and strong and weak forces thatthe standard model of particle physics incorporates a large amountof of symmetry. Unfortunately, Einstein's theory of general relativity isnot consistent with quantum mechanics and so cannot be simplycombined with the standard model to provide a consistent theory ofall the four forces.It is widely believed that supersymmetry, which is a symmetry thatexchanges fermions (matter particles such as the electron) withbosons (force carriers such as photons of light) will play animportant 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 dimension 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 theoryare unique as a consequence of the large amount of symmetry, and inparticular supersymmetry, that they possess. These are the so-calledsupergravity 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. This complete theory is known as M-theory. Although little is known about it on microscopic level it is known to involve eleven-dimensions, extending the ten-dimensional space-time of superstrings.We wish to find and understand this underlying theory of string andbranes. We propose to investigate this very intricate theory fromseveral points of view. The first is to understand the theory at lowenergies, where it must produce space-time and the four forces weknow. Secondly, we will investigate the theory at very highenergies, where its fundamental constituents behave like vibratingstrings and branes and the notion of a smooth space-time does nolonger make sense. Our most important tool will be the enormous amount of symmetry thatthis theory is thought to possesses. Symmetry is a sign ofunderlying simplicity and beauty and has been a reliable guidingprinciple in reaching the understanding of physics we have today. Inthis process we expect to replace of our usual notion of space-timeby one which is consistent with such symmetries. This illustrates onthe one hand the profound effect that a unified theory has on ourunderstanding of nature, and on the other hand the central roleplayed by symmetries.