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 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 attempting to describe black holes or 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 must be replaced by 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 challenges, 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 will be of use to fully understand 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 proposed in this application by the Centre for Research in String Theory (CRST) addresses foundational questions in theoretical physics. There are direct societal and cultural impacts of this work. The general public has a long held fascination with work that explores the basic building blocks of nature and challenges our understanding of the world around us; engaging the public with science is a critical element in ensuring the progress of society, and within this, inspiring the next generation of scientists is essential to ensuring successful societies of the future.

Culturally, reflecting this intrinsically human view point, artists have sought out the latest research results in theoretical physics to provide a stimulus for their work. In some cases works and exhibitions have been directly inspired by contemporary developments in theoretical physics. This continues with artists that are hungry for ideas and a society that is more open to abstract cultural constructs.

The CRST continues to work to provide these direct societal impacts for its research through a variety of engagement activities within two main strands. One is direct public engagement where the results of the research are brought directly to the public through various media, including web based material using professional outreach specialists. The goal is to reach a large number of people with a wide demographic spread. This will be achieved through partnerships with known internet "brands" that have a high readership. Other work with teachers will provide material for them to move beyond the syllabus and provide pupils with inspiring ideas from the forefront of physics.

The other strand of impact work is to develop the engagement with the arts and to directly inspire cultural works based on research outputs. Our previous successes in this arena will be built upon with planned future exhibitions and artist collaborations. As part of this it is crucial not just to collaborate with artists but also to be involved with stakeholder organisations such as galleries. As such we will continue to have gallery-based events that bring physics to a non-traditional audience. This engagement work is ultimately about having an impact on how artists see the world and how this change is reflected in their works.

In addition to these areas of impact work that expand upon past approaches that we have found to be successful, we will be instigating a third new strand focussing on the development of a set of techniques that may be applicable to other problems with direct economic benefits. A recent example has been the use of relativity-based techniques in optics, which has the potential to subsequently lead to the production of new medical applications. Through sustained engagement with a variety of businesses we intend to exploit such spin off techniques where there is a clear application. The key to finding these applications comes from a regular exposure to problems posed by business partners. We have launched a new Business Club initiative in order to provide a regular forum to do this.