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

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
standard model in 1967, it has so far not been possible
to 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 cannot 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 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 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. 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 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 space-time 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 space-time 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 space-time
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.

The proposed research will benefit most directly those working on
theoretical physics, in particular on supersymmetry and string
theory and more generally those seeking to find a single consistent
theory of physics. There are several research groups working on these topics within the UK and many more worldwide. The work involves some of the latest mathematics, hence is also
relevant to mathematicians, in particular those working on group
theory and geometry. However, such research also has direct
relevance to those working on the following fields: the strong nuclear force, the formulation of explicit phenomenological models of
particle physics, and the formulation of cosmological models of inflation and dark
matter. Thus it can also lead to benefits for model builders working on particle physics and astronomy. We have discussed the impact on these groups in the section `academic beneficiaries'.

Past work on theoretical physics has, with the fullness of time, been of considerable use to society either as a direct result of
the new physics found or as a consequence of the new mathematics and
technical developments that where developed. This has lead to a direct technological input into industry.

Industry also benefits from the training of young researchers in the ability to solve hard and complex problems. The theoretical physics group at King's has trained many younger researchers who have later entered the financial and other sectors
of the economy to apply their problem solving skills. In particular, by funding cutting edge science the UK attracts younger intellectual talent from both within and outside the UK. And although some carry on in UK academic life, a substantial number take non-academic jobs in the UK, thus providing the economy with highly trained people. Such spin-offs from fundamental science have long been vital to the international economic and industrial competitiveness that the UK enjoys. Indeed, a crucial feature of the modern UK's economic and social wealth is its international reputation as a world leader for independent thinking in both the academic and industrial sectors.

In addition to these economic factors, the general public has strong interest in the fundamental questions about our Universe. For example Lambert's work on M2-branes has appeared in the book `Solar' by Ian McEwan, showing a direct impact of the group's research into contemporary culture. The general public will therefore benefit from a deeper and continuing investigation into Nature at its smallest scales.

In summary, the UK can be proud of having one the worlds most prestigious and world leading scientific traditions which has long been a cornerstone of the UK's intellectual health, economic wealth and culture. We believe our proposed research is very much a part of this.