Fundamental Implications of Fields, Strings and Gravity

Newtonian physics describes our universe well, provided the objects of interest are not too small, do not move too fast, or are not too dense. At a small length scales, Newtonian physics is replaced by quantum physics. In addition, if interactions involve speeds close to that of light, then quantum physics is replaced by quantum field theory (QFT). This theory is a milestone of scientific discovery and underpins all experimentally verified particles and interactions. The standard approach to QFT relies on perturbation theory, which assumes that all interactions are weak. There are many situations where that is not the case, and the resulting theory is said to be strongly coupled. In the theory underlying the standard model of particle physics the interactions are generally not weak. This prevents us from explaining phenomena such as the confinement of quarks to form the protons and neutrons that make up matter. This is a conceptual problem, and a major limitation for phenomenological applications.

What about if we are dealing with extremely dense objects? For example, if all of the matter inside the Earth were compressed to fill a sphere with a radius of a few millimetres, then the above theories would break down. In this case, one would need to incorporate Einstein's theory of general relativity with quantum field theory. However, there is no completely consistent way to do this, leaving a gaping hole in our understanding of the universe.

The only theory that successfully combines QFT with general relativity is string theory. Self-consistency of the theory demands stringent mathematical conditions be imposed. For example, there must exist six extra spatial dimensions in addition to the three spatial dimensions we are accustomed to. To resolve this, one must ``compactify'', i.e. posit that the extra dimensions span curled geometries, not visible to present day experiment. A rough analogy is with a hose: from a distance it looks one-dimensional, but on closer inspection there is an additional circular direction. Describing the physics of the observable universe becomes a problem closely tied to the geometry of certain spaces.

Remarkably, string theory has led to new ideas concerning the description of strongly coupled QFTs. One such tool, known as holography, represents the idea that our space-time encodes information of a higher dimensional one, much like a hologram is a two-dimensional representation of a three-dimensional picture. It turns out that the strongly coupled QFT in four-dimensions relates to a weakly coupled five-dimensional gravity theory in which we may apply perturbative techniques to perform computations. Over the past decade, this idea has led to many new and exciting developments in theoretical physics. It has also been used to understand experimental results obtained under extreme pressure and temperature conditions (quark gluon plasma).

The aims of this project are two-fold: to use these new tools from string theory to understand the strongly coupled regime of QFT; and to use string theory to model the four-dimensional space time observed today. For example, many of the ideas and concepts within string theory have drastically changed the way we think about strongly coupled QFTs. There are also new examples of strongly coupled QFTs, in which calculations have become tractable. Although not realistic models, they share with the real world many common qualitative features, which are otherwise hard to understand. By studying these new examples we hope to shed light on how obscure mechanisms such as confinement work in theories of experimental interest. By utilising these developments in quantum field theory we hope to undercover the exact conditions required to reproduce the string compactification that describes modern particle physics.

This research proposal aims at making progress towards the understanding of fundamental questions in theoretical physics. It will primarily impact researchers working in particle physics. It combines ideas and concepts from various fields, and consists of numerous themes of significant interest to physicists outside the discipline of particle physics, as well as mathematicians working in areas adjacent to string theory. Our work will therefore have a considerable academic impact, both in the UK and abroad.

Members of the Fields, Strings and Geometry group will disseminate their knowledge and expertise by engaging with the academic community via seminars and conferences. They will also extend their collaborative networks with academics in the UK and internationally, and further improve their already very strong record of writing papers and review articles published in high-impact international journals. All this will further develop the UK research area.

More broadly, this proposal will contribute towards improving the UK science environment in general. The advancement of fundamental sciences is one of the significant landmarks in the development of modern societies.

The training which our PhD students receive will result in a particularly beneficial transfer of knowledge, which will be enhanced by the breadth of expertise in the group, and our collaborative work. Our PDRAs will also benefit in this context. The work environment is ideal for young researchers to increase their experience and undertake topical research in many areas. We will also construct new courses in theoretical physics at an introductory level, and present lectures at summer schools. This training is important irrespective of whether the researcher remain in academia; it will aid them if they choose to move into other highly skilled careers such as finance or the high-tech industry. These are all vital and valuable components of the UK economy. Therefore, this proposal will contribute to the UK's cultural and economic well-being.

Further outcomes of the proposed research are likely to impact on society in diverse ways, often in the longer term. For example, the study of quantum mechanics in the early 20th century was at the time a similarly fundamental science with no obvious, nor immediate, benefits to society. Today, quantum mechanics underpins all of modern solid state electronics, governing the behaviour of super-computers to GPS satellites. It is likely that the outcome of our research could benefit society in a similar fashion, once the technology has been sufficiently well developed to be applied.

There has been a burgeoning public interest in fundamental science. For example, television programmes on the BBC such as episodes of Horizon, `What happened before the Big Bang', and the documentary `Beautiful Equations.' There are also radio and television personalities such as Prof Jim Al-Khalili (Univ. of Surrey). It is of great importance to increase the awareness of scientific scholarship to the wider public. In view of this we have applied for various programmes to extend departmental outreach activities to local schools and the general public. Our group members have given numerous public lectures to engage with the public. We will continue with this by giving public lectures at schools to attract pupils to study in mathematics and physics. We will also present our research in an accessible form to the public, using our website. This will benefit the public by increasing their understanding of science, and encouraging future generations to pursue pure science. In turn, with a scientific training, future generations of the UK will be more highly educated and able to compete at the highest levels in an increasingly scientific world society.