Geometry for String Model Building

The main purpose of the research proposal "The Particle Physics and Cosmology of Supersymmetry and String Theory" is to create a strong UK research effort exploring the mathematics and physics of string compactifications. The proposed work has strong interdisciplinary aspects and will feed into particle physics and cosmology. This is facilitated by a wider, international collaboration which involves Oxford University and Imperial College in the UK, Ludwig-Maximilian University/Max-Planck Institute Munich and University of Hamburg/Desy in Germany and the University of Pennsylvania and Princeton University in the US. Accordingly, this proposal to EPSRC is accompanied by related proposals to DFG in Germany and NSF in the US.

String theory is an area of research at the interface between physics and mathematics. It relates to and has indeed inspired cutting edge mathematics and at the same time it remains the most promising candidate for a unifying physics theory. Via string theory the study of geometry - covered by the mathematical areas of differential and algebraic geometry - is directly related to properties of physical theories, such as their particle content or their associated cosmological evolution. For example, in some constructions, the Euler number, roughly counting the number ``holes" in the geometry, also determines the number of families of fundamental particles in the associated physical theory. This link has led to a fruitful interaction between physics and mathematics, with advanced mathematical methods being applied to analyse string theory models on the one hand and physical insights inspiring new mathematical developments on the other hand.

The theme of the proposed international research is at the centre of this interdisciplinary area. Progress in string theory crucially relies on understanding how advanced mathematical methods can be applied in concrete string theory setting. It also requires further developing these methods as well as creating new mathematical structures. In pursuing these lines of investigation, the main goal of the proposed programme is to lay the groundwork for answering one of the main question in contemporary science: Is string theory indeed a viable unified theory of physics?

Research in string theory, just as research in closely related fields of pure mathematics and in theoretical particle physics, can obviously not be linked to direct and immediate economic benefits. However, it is worth remembering that, historically, is has often taken decades for fundamental physics theories, such as electromagnetism, quantum mechanics or general relativity, to translate into direct benefits for society - yet modern life would be unthinkable without the technology based on these fundamental theories. Analogous remarks apply to major developments in pure mathematics. In short, there is convincing historical evidence that funding of mathematical physics and related areas is an extremely worth while long-term investment.

On a more immediate level, the quest for a fundamental theory of nature and its mathematical formulation is well embedded into the public consciousness and is considered one of the major cultural and intellectual issues of our time. The main goals of the proposed research programme are closely related to these fundamental questions.

Fundamental research in theoretical and mathematical physics is pursued by all developed countries and underpins a range of more applied subjects. No university can claim to be a leading research institution without substantial activities in the subject. Hence, the world-class status of many UK higher educational institutions - their success in attracting talent from across the world and their contribution to the UK economy - depends on support for such theoretical and fundamental sciences.