Particles, Fields and Spacetime

宇宙中的所有物质和除了引力之外的基本力似乎都可以用量子场论很好地描述，在量子场论中，物质的基本成分是点状粒子，它们通过交换其他种类的粒子来相互作用。对量子场论的实际理解，使我们能够在许多感兴趣的情况下进行计算，是在五十多年前建立起来的；然而，我们仍然没有完全理解量子场论中隐含的结构，最近的工作已经开辟了完全不同的计算方法。对称性在我们目前对量子场论的理解中起着核心作用。我们工作的一个分支是研究具有超对称性的理论：这给理论的结构提供了强有力的约束，使我们能够理解可能理论的空间结构。在理论中作用于扩展对象的新对称性被称为广义对称性，最近为量子场论提供了一个新的视角；事实证明，许多熟悉的理论都概括了对称性。量子效应对对称性的破坏，被称为异常，也为相结构提供了强大的约束。我们正在研究与广义对称相关的异常，扩展我们对低能理论中可能相的理解。场论中关键的可观测数据是特定过程的振幅。在某些理论中，这些振幅具有令人惊讶的简单结构，很难从标准场论方法来计算它们。我们正在从新的物理和数学角度探索这些结构，这可以帮助我们更深入地理解场论。看来我们需要超越这幅图来考虑重力。描述量子引力的一个激进的提议，称为全息，将引力理论与一类存在于更少维度的量子场论联系起来。场论中的一些难题可以映射到高维空间中更简单的问题。这也提供了一个关于时空的新视角，可以用来加深我们对引力的理解。我们正在研究这些技术在用于研究有趣的新物质相的场论中的应用，我们正在探索场论内在量子力学特征在高维几何的出现中的作用。

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.