Amplitudes, Strings and Duality

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It is widely believed that particles are the fundamental building blocks of our universe. Over many decades increasingly predictive models were developed based on the assumption that matter, which interacts via specific forces, behaves like pointlike particles down to the tiniest scales. These successes are neatly summarised in the "Standard Model" (SM) of particle physics, and since the discovery of the Higgs at the Large Hadron Collider (LHC), we are tempted to consider it to be 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 universal language of particle physics, is applied to gravity, the results are disastrous. In particular, many calculations done in this framework lead to meaningless infinities. This poses a major challenge, since any theory attempting to describe black holes or the early universe must be able to unify QFT and gravity. In the spirit of much of modern physics, it is thus natural to conclude that the SM is an "effective theory" which is only valid 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 and even higher-dimensional objects called "branes". Although this solves the problem of unifying 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. Research at the Centre for Research in String Theory (CRST) at Queen Mary University of London focuses on understanding QFT, string theory and their interconnections. The range of activities 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 quickly intractable, and can not be done in a reasonable amount of time even on powerful computers. The techniques pioneered by the CRST are shortcuts for calculating these amplitudes which evade the complications of traditional methods. Finding better methods for such calculations remains an important problem, since these will be of use to fully understand LHC results or to model gravitational waves recently discovered by LIGO.Many of the theories mentioned above can be realised within the context of string theory. 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 crucial 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 quantities of interest, e.g. scaling dimensions, indices, and partition functions. These techniques are known for only a small subset of theories, however, and developing tools for broader classes of theories remains a pressing problem. The CRST has made significant contributions to the understanding of holographic dualities in string theory, relating gravitational to non-gravitational theories, while making new connections to chaos and quantum information, which have opened up novel research directions. It has led the study of a rich array of generalizations of geometry and field theory, a present focus being exceptional field theories and their implications for the structure of M-theory. 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.