Geometry, holography and Skyrmions

Particle physicists have a good understanding of the fundamental constituents of matter, but the mathematical complexity of their theory means that, even with the use of supercomputers, it is impossible to use it to predict even the basic properties of even the simplest atoms familiar from everyday life, such as helium, carbon and oxygen. Fathoming the core of these atoms is the realm of nuclear physics, but current approaches are detached from fundamental theory and instead are mainly based on fitting phenomenological models to experimental data. The ambitious aim of this project is to provide a link between fundamental theory and nuclear physics through a novel mathematical description, using a geometrical formulation, in which atomic nuclei arise as stable localized excitations called Skyrmions.

Particle physicists have a good understanding of the fundamental constituents of matter, but the mathematical complexity of their theory means that, even with the use of supercomputers, it is impossible to use it to predict even the basic properties of even the simplest atoms familiar from everyday life, such as helium, carbon and oxygen. Fathoming the core of these atoms is the realm of nuclear physics, but current approaches are detached from fundamental theory and instead are mainly based on fitting phenomenological models to experimental data. The ambitious aim of this project is to provide a link between fundamental theory and nuclear physics through a novel mathematical description where atomic nuclei arise as stable localized excitations called solitons. Such a description of atomic nuclei would have a tremendous impact, particularly
in the study of nuclear matter under extreme conditions. A thorough understanding of nuclear matter is vital for harnessing the energy source offered by nuclear fusion, which has the potential to offer an almost limitless source of energy with minimal environmental impact. There are still great challenges to overcome before fusion becomes a viable source of energy for the future. As well as funding direct research into the (so far, formidable) technological challenges of fusion, it is vital
to support fundamental research into extreme nuclear matter, as an unforseen insight here may well suggest a smart route around some of the outstanding engineering obstacles. The chief impacts from this research will be fundamental scientific knowledge and the training of young scientists to develop world leading skills in mathematical science and its advancement through parallel computation. It will therefore make a positive impact on the high performance computing capability of the UK.
The applicability of these skills goes far beyond this specific project and they are highly-valued by both academics and industry, being core skills in modelling virtually every physical, technical, or biological process, from climate change to cancer. This project is well-suited to make an impact in improving the public understanding of scientific discovery through computational mathematics. Soliton results on the shape and distribution of nuclei are ideal for presentation in a visual format that is immediately engaging for a general audience, and the visual results are often aesthetically pleasing in their own right.