Amplitudes, Strings and Duality

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. For instance, the SM does not account for gravity and it is particularly difficult to include this force in the framework of quantum field theory (QFT) which is the universal language of particle physics. 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 such as string theory.

Research at the Centre for Theoretical Physics (CTP) 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 CTP has found and developed novel techniques for calculating scattering amplitudes. These are necessary because the usual calculus of Feynman diagrams becomes quickly intractable, and cannot be done in a reasonable amount of time even on powerful computers. The techniques pioneered by the CTP are shortcuts for calculating these amplitudes which evade the complications of traditional methods and shed new light on surprising structures that allow to connect amplitudes of different theories. Unexpectedly these new computational techniques can be applied to problems outside the particle physics domain, such as the study of binary black-hole systems. The CTP has contributed to this recent development both by developing the general framework and by improving on the precision of the results in explicit applications. Finding better methods for calculating scattering amplitudes remains an important problem, since these will be of use to fully understand LHC results and to model gravitational waves recently discovered by the LIGO and Virgo collaborations.

String theory offers unexpected insights into quantum field theories, such as holographic dualities between gravitational and non-gravitational theories, with the potential to provide novel ways to understand QFTs in challenging regimes. The CTP has continued its leading role in holography, with algebraic approaches that illuminate its mechanisms, computations of new correlators linking conformal field theory to anti de Sitter space, and the development of integrable segmented strings. Its recent results in QFT, e.g. on quantum codes and CFT operators, Galois transformations and quantum mechanics on graph algebras, are converging to provide novel perspectives and research directions on the role complexity and quantum information have in string theory. This is forming part of new dialogues between string theory and artificial intelligence, where machine learning methods are being applied to QFT and strings, while the stringy mathematics of new matrix models is providing tools for data sciences. The CTP will build on its leadership in extended geometry and non-perturbative approaches to M-theory as well as QFT.

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.