String Theory, Gauge Theory and Duality

That our universe is made out of particles is often taken for granted. For nearly a hundred years, we have had increasingly predictive models based on the assumption that, at very small scales, matter behaves as point particles which interact via specific forces. These forces, as well as the nature of the particles upon which they act, are the "Standard Model" (SM) of particle physics.
Since the discovery of the Higgs last year at the Large Hadron Collider (LHC), it is perhaps tempting to consider the SM a complete description of the universe at its smallest scales.

However, this is not the case. In particular, the SM does not account for gravity. When quantum field theory (QFT), the calculational language of particle physics, is applied to theories with gravity, the results are disastrous. In particular, many calculations done in this framework lead to unfixable divergences. This is a problem, since any theory of the early universe will need to sensibly combine both QFT and gravity. In the spirit of much of modern physics, it is thus reasonable to guess that the SM only works up to some energy scale, after which it becomes a bad approximation to a more complete theory.

The leading candidate for this underlying theory is String Theory, which proposes that matter is not made of point particles, but one-dimensional strings (as has become clear, this theory also has higher-dimensional objects called "branes"). Although this solves the problem of combining gravity with the SM, it also presents new issues, such as the existence of extra spatial dimensions. Understanding how to interpret these predictions is necessary if string theory is to be taken seriously.

The Centre for Research in String Theory (CRST) at Queen Mary, University of London has been instrumental in understanding string theory and its consequences for QFT. The current focus of the group is broad, dealing with issues in both QFT and string theory alike. On the QFT side, the CRST has found novel techniques for calculating scattering amplitudes. These are necessary because the usual calculus of Feynman diagrams becomes complicated quickly, and can not be done in a reasonable amount of time even on a computer. The techniques pioneered by the CRST are shortcuts for calculating these amplitudes which evade the complications of traditional methods. Finding better techniques for such calculations remains an important problem, since these results may be necessary for understanding LHC results.

Many of the theories in the previous paragraph occur within the context of string theory, and can often arise on branes. Although such theories are complicated, it is possible to use both field and string theory techniques to get results that do not rely on perturbative techniques. This is necessary because such theories often do not have expansion parameters. The CRST has been at the forefront of understanding such theories, and has developed new tools for calculating the quantities of interest, e.g. scaling dimensions of operators. These techniques are known for only a small subset of theories, however, and developing such tools for broader classes of theories remains a pressing problem.

The CRST has also made significant progress in understanding string theory in its own right. Geometries that appear in string theory exhibit surprising new dualities that relate very different mathematical spaces. The study of these dualities is of interest to string theorists, since the field still lacks a complete understanding of the space of stringy geometries.

Many of the above topics fall under the classification of using string theory as a tool for understanding difficult problems in QFT and particle physics. Even if string theory turns out not to be the correct short-distance completion of the SM, its use as a tool for solving problems in QFT is secure.

The research done by CRST provides the foundation and inspiration for our engagement with schools, alumni, the general public and the art community in promoting the understanding of and interest in science. Schools talks on extra dimensions, which form an essential part of string theory and also provide one of the theoretical scenarios for investigations at the Large Hadron Collider, never fail to fascinate, intrigue and provoke questions. An interest in science at school level often translates into a science degree, which provides the background for careers in pure or applied science. For the general public, an awareness of science contributes to a sense of wonder at the mysteries of the natural world as well as an understanding of the power of organised, logical and mathematical thought. Policy makers can draw on scientific successes to promote well-thought out, logically sound avenues for progress in society.

The research proposal is relevant to beneficiaries outside our immediate academic circle. The theoretical investigations of the structures of amplitudes have many practical applications to particle physics and in particular to the LHC, and the study of string theory and its underlying geometry makes unexpected connections with, and surprising extension of certain branches of mathematics e.g. number theory and algebraic geometry.

The training of PhD students in string theory is probably one of the most demanding in the academic world due to its very mathematical nature and the highly competitive nature of the field. Unsurprisingly, the skills obtained by our PhD students are also in high demand outside academia, and many of our graduates who choose not to remain in academia find high-level work in companies such as banks, investment companies and in R&D, and contribute to the success of these companies. The CRST is planning in particular to intensify our links with companies in the financial sector.

The CRST has also has a significant knowledge exchange with the art community. Activities, in which members were involved include: the 2009 Frieze art fair and talks at the Tate Modern, the Royal College of Art, the Core gallery, the Korean Institute of Advanced Study and the Institute of Contemporary Art. Berman of CRST is collaborating with Turner prize winner Grenville Davey on sculptures inspired by duality and string geometry, which have been exhibited at the Isaac Newton Institute and the Launch Pad (Royal College of Sculpture). This work is further supported by the Henry Moore foundation and the Westfield Trust. Another example is a recent presentation by the artists Flow Motion at the Dana centre, which was inspired by dualities in physics. Over the years the activities in this area have evolved into a broad programme of engagement with the arts community on the foundational questions that we investigate. For the future various activities are planned e.g. an exhibition at the Ruskin Gallery in Cambridge, and a public lecture at the Espacio Gallery.

The work of this proposal will also be promoted to school, teacher and community audiences through our ambitious and on-going outreach programme including: refresher courses and teaching material for school teachers, school talks, taster courses, school student visits to the College, and special lectures and events. The outreach activities of the School of Physics and Astronomy are coordinated by two staff members and are further enhanced as part of the South-East Physics network, which is running an extensive series of events. The research of this proposal is highlighted in these outreach events, which stress the important contributions of our research. Staff members, RAs and PhD students play an integral part in delivering these activities. Extensive web based material for schools is now being developed with the Millennium Maths project in an STFC funded partnership. Finally, members of the CRST are running a programme of talks for alumni of the School.