Investigations of particles, quantum fields and extended objects

We are interested in what is happening to the smallest bits of matter, how
they interact with each other, what a force really is, and how all of this
fits into what we observe around us in the universe. We have a very good
theory that describes all this for many of the particles and interactions
(quantum field theory). By and large, the
measurements line up with the predictions and this is a significant scientific
achievement. However, there are large holes in our knowledge and this leaves
oppurtunity for work by our research group.

For instance, in the centre of atoms lies the nucleus. The nucleus is strongly
bound, which means that we don't know how to calculate anything analytically
(with a pen and paper) using the standard techniques.
Our research has found a clever way of mathematically modelling the nucleus
using analytic techniques: the Skyrme model. Now, we can describe all nuclei
from atomic number 1 to 108 using this model. We shall be exploring the
mathematics behind this in more detail: it has a connection to gravitational
theories and string theories (mathematical theories that model particles as
tiny quantum loops).

There are also other particles other than nuclei which
are strongly bound, such as B-mesons.
For these, sophisticated computer programs must be
built which break space and time up into a grid of points, and the quantum
fluctuations of the sub-nuclear interactions are simulated using random
numbers on this lattice. Analytic calculations must be done to match the
numbers obtained on the computer to experimental data. We shall develop these
calculations, and perform new ones so that data can be used to extract the
level to which various quarks (for example, the up quark and the b-quark)
mix. This helps provide an accurate description of an unexplained phenomenon:
how the funny pattern of quark mixing comes about. These calculations also
help the extraction of the difference between matter and anti-matter from
experimental data.

String theory is an extraordinarily mathematically rich structure, that
purports to describe gravity. One variant of it may also even underlie all of
the interactions between particles that are observed in nature. The tiny loops
behave like particles unless one probes them at energies that are far too high
for us to reach in current experiments. Some of our research examines the rich
structure behind the mathematics of these theories: it turns out that
scattering two particles and scattering three particles have strict relations
between the interaction probabilities. Sometimes, truths such as these are
easier understood by mapping one string theory to another one, which has a
different coupling strength and a different number of space-time
dimensions. These "dualities" help us winkle out truths and
deep connections in string theory. We shall be investigating their role in the
relations between interaction probabilities.

The LHC will start up again after the shut-down around 2015 with double the
energy that it had in 2012. This means that if supersymmetry keeps the higgs
light (this is the main motivation for the kind of supersymmetry that the LHC
can discover), the LHC should discover supersymmetric particles in the first
year of running. Even if this idea of supersymmetry is not present in nature,
some other particles or interactions should be responsible for cancelling the
quantum fluctuations (a seething random mass of particles popping in and out
of existence) which tend to make the Higgs mass some 10^15 times heavier than
has just been observed at the LHC. These particles should also be discovered
soon. We shall be interpreting the data, and discriminating various models by
comparing their predictions to any signals that the LHC sees. We should be
able to work out which theories are ruled out, and which are favoured.

We will communicate the results of our research to the general public and to
school children. Our goal is to both educate and to inspire, to explain the
wonder of
the natural world, the excitement of being involved in cutting edge research
and the joy of understanding something that no one else on the planet
knows. Members of the group have media connections through radio, television,
print and the internet and we will continue to develop these.
Members of the group have been very active in promoting their work and physics
more generally. This
includes interaction with researchers in other disciplines, education at the
University level and outreach, both to public and to schools.
Details of recent
outreach activities can be found in the Pathways to Impact document.

We teach ``Part III", a one year Masters degree course that attracts 250 of
the best mathematics and physics students from all over the world. Our
courses on theoretical physics are routinely attended by over 100
students. While we appreciate that teaching is a core University activity, we
wish to highlight the fact that Part III is recognised as one of the most
influential courses worldwide in fundamental physics training. It raises the
UK's international profile and helps recruit graduate students for the UK as
a whole. A google search for "Quantum Field Theory" (or even just "QFT")
brings up the extensive Part III lecture notes in a prominent position, while
videos of Tong's quantum field theory lectures are available on YouTube
and the first in the series has been viewed around 50,000 times. Moreover,
Part III provides a forum in which the latest research results can be
directly communicated to a large number of students (e.g. lectures on the
applications of AdS/CFT).

Our educational activities stretch beyond the UK. Various members of the group
have been engaged in starting a Masters course at the Perimeter institute in
Canada. Dunajski has been heavily involved in mentoring mathematical
research in sub-Saharan Africa, working
closely with the maths department in Accra, Ghana and advising PhD students
and young faculty members. This work is
covered by an LMS grant. Quevedo has set up a PhD programme
at the ICTP for promising students from developing countries.