Particles, Fields and Spacetime

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All matter in the universe and the fundamental forces apart from gravity appear to be well described by particle theories, in which the fundamental components of matter are pointlike particles, which interact by exchanging other kinds of particles. Quantum field theory is the mathematical language describing these particle theories; the particles describing forces are described by a class of theories called gauge theories. A practical understanding of quantum field theory, which enables us to do calculations in many circumstances of interest, was constructed more than fifty years ago; however we still do not have a complete understanding of the structures implicit in quantum field theory, and recent work has opened up radically different approaches to doing calculations. It has been understood that certain gauge theories have additional previously unsuspected symmetries, which explain the mysterious simplicity of some computational results. This has been developed to obtain more efficient calculational techniques for increasingly general questions. In an independent line, a symmetry called conformal symmetry has been newly exploited to constrain the particle content and interactions of theories with this symmetry. We aim to develop these tools further and bring them together, leading to a deeper understanding of the calculation of interactions of particles in the vacuum. We will also study the theory in situations with finite density, classifying phases of matter. Symmetries play an important role here, and the breaking of symmetries by quantum effects, referred to as anomalies, provides powerful constraints on the phase structure.It appears we need to go beyond quantum field theory to include gravity. The leading candidate for this extension is string theory, which is based on the idea that the particles are actually one-dimensional loops of string, with the interactions described by smooth surfaces connecting different strings. Work on string theory has led to the discovery that some quantum field theories can be related to string theories in a space with more dimensions; this is referred to as holography. Some difficult questions in the field theory can be mapped to simpler questions in the higher-dimensional space. This also provides a new perspective on string theory, which can be used to deepen our understanding of gravity. We are studying the application of these techniques to field theories used to study interesting new phases of matter, and we are exploring the role of intrinsically quantum mechanical features of the field theory in the emergence of the higher-dimensional geometry. Cosmology is the study of the universe as a whole. The overall geometry of the universe is expanding on large scales. In the very early universe, there appears to have been a period of exponential expansion, called inflation. We are interested in the behaviour of quantum fields during this inflationary period, which we will investigate using an approach called stochastic inflation. We will also apply holographic methods to the description of the very early universe, enabling us to apply well-developed field theory tools to inflation. Black holes can be produced in the very early universe from fluctuations of the density of matter; we will study the formation and dynamics of these primordial black holes. These may be interesting as candidates for dark matter, a kind of matter required to explain observations of the large-scale dynamics in the universe today.