Particles, Fields and Spacetime

All matter in the universe and the fundamental forces apart from gravity appear to be well described by quantum field theories, in which the fundamental components of matter are pointlike particles, which interact by exchanging other kinds of particles. 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. Symmetries play a central role in our current understanding of quantum field theory. One branch of our work is the study of theories with supersymmetry: this gives strong constraints on the structure of the theory, allowing us to understand the structure of the space of possible theories. New symmetries which act on extended objects in the theory, referred to as generalised symmetries, have recently provided a new perspective on quantum field theory; it turns out that many familiar theories have generalised symmetries. The breaking of symmetries by quantum effects, referred to as anomalies, also provides powerful constraints on the phase structure. We are studying the anomalies associated with generalised symmetries, extending our understanding of possible phases in the low energy theories. The key observable data in field theories are the amplitudes for particular processes. In certain theories, these amplitudes have surprisingly simple structure, which are hard to understand from the standard field theory approach to calculating them. We are exploring these structures from new physical and mathematical perspectives, which can help us to understand field theory more deeply.

It appears we need to go beyond this picture to include gravity. A radical proposal for the description of quantum gravity called holography relates gravitational theories to a class of quantum field theories living in fewer dimensions. 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 spacetime, 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.