Bootstrap and Uniqueness for Form Factors and the S-matrix

Project Information

BUFFS

Grant agreement ID: 101025095

DOI

10.3030/101025095

Project terminated on 30 November 2023

EC signature date 28 April 2021

Start date 1 September 2022

End date 31 August 2024

Funded under

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Total cost

€ 224 933,76

EU contribution

€ 224 933,76

Coordinated by

QUEEN MARY UNIVERSITY OF LONDON
United Kingdom

Periodic Reporting for period 1 - BUFFS (Bootstrap and Uniqueness for Form Factors and the S-matrix)

Reporting period: 2022-09-01 to 2024-08-31

Summary of the context and overall objectives of the project

The project “Bootstrap and Uniqueness for Form Factors and the S-matrix”, or “BUFFS”, carried out by Dr Rodina Laurentiu, under the supervision of Prof. Andreas Brandhuber at Queen Mary University of London, aimed to provide new insight into the mathematical structures of Quantum Field Theory (QFT). QFT is the mathematical framework used to describe Nature at the most fundamental level, particularly through scattering amplitudes, which encode how elementary particles interact with each other. However, scattering amplitudes are still far from being completely understood. Recent progress has shown that scattering amplitudes contain a much a richer structure than previously thought, which may even help us in the quest to fully understand even the most extreme phenomena in our Universe, such as black holes or the Big Bang itself.

The project was aimed to investigate such novel structures, and lead to a deeper understanding of scattering amplitudes. The concrete aims of the project were divided into three tasks, focusing on aspects in which Dr Rodina and members of QMUL could contribute their complementary expert knowledge. The first task was to understand why completely different physical properties of amplitudes, such as their low energy (infrared) or high energy (ultraviolet) limits seem to contain identical information. Solving this mysterious equivalence could potentially lead to a radical new definition of amplitudes, and ultimately of QFT. A second task involved understanding what properties of scattering amplitudes may be carried over to form factors, which are slightly more general objects than scattering amplitudes. The completion of this work would demonstrate that methods of scattering amplitudes, and recently discovered mathematical structures, can be much more generally applied to QFT. A third task involved mapping out the space of theories compatible with fundamental principles. Theories can be described by various parameters, which reflect the strength of particle interactions, or their masses for instance. However, not all values of these parameters lead to consistent theories.

At its completion, the project led to several important results in the field. It showed that naively independent amplitude properties are closely connected, potentially bringing closer a complete reformulation of scattering amplitudes. It demonstrated the universality of Hopf algebras, a newly discovered property of certain amplitudes, which may finally explain a strange connection between different physical theories, including gravity. And finally, it showed that the space of allowed Conformal Field Theories can also be described by methods originally developed for scattering amplitudes.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

Working on the first research task, Dr Rodina found that a newly discovered property, called amplitude zeroes, can be used to explain the mysterious equivalence between the IR and UV behaviour. Calculations carried out for this task showed that this new property implies the observed IR and the UV behaviours, promising a completely new understanding of amplitudes, including more efficient computational methods. Work on the second objective also benefited from an unexpected breakthrough, when a team at Queen Mary University of London, including the project supervisor, Prof. Andreas Brandhuber, and co-supervisor senior lecturer Dr Congkao Wen, uncovered a potential new structure called Hopf algebras. Together with Dr Wen, and Dr Chen, a former QMUL postdoc, Dr Rodina proved that these algebras are much more universal than previously thought and used them to propose a general formula for scattering amplitudes of gluons. For the third objective, related to the geometrical description of theory space, much of the work focused on applying the approach to the Conformal Field Theory bootstrap. Dr Rodina and collaborators were able to use this approach to solve the longstanding problem of integer-degeneracy.

Dr Rodina’s work was communicated with the scientific community on several occasions, including at the annual conference Amplitudes, in Prague in 2022, followed by a workshop also in Prague, in 2023. Dr Rodina was also invited to give seminars in Paris, Zurich, Taipei, and Beijing. As outreach activities to present research to non-expert audiences, Dr Rodina participated in a group exhibition in Timisoara. This involved creating an artwork titled “A fragment of a future sculpture” together with artist Andreea Albani, utilizing the programming language used in his research. During a planned short visit to Beijing, Dr Rodina also had the opportunity to discuss his research and gain specialist advice with academic community and disseminate the project’s findings at Tsinghua University, Beijing, and Normal College of Hohhut including with students.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The fellowship pushed the state of the art in several new directions, achieving both initial goals, and dynamically incorporating new directions as the rapidly evolving field lead to new discoveries during this time. First, the work carried out identified the new and important property of amplitude zeros as the missing ingredient to connect the IR and UV. This now strongly suggests a complete reformulation of scattering amplitudes should be possible, by using these equivalent defining properties as starting point. It also demonstrated that Hopf algebras are a universal and central structure of scattering amplitudes, and that the colour kinematic duality may be better understood from this perspective, ultimately explaining why gluon and graviton amplitudes are so closely related. Finally, the project showed how the tools developed for scattering amplitudes can be relevant in the CFT bootstrap and enabled for the first time the solution of new problems, such as integer-degeneracy, previously beyond the reach of traditional approaches. Overall, these results bring new connections to research in mathematics, and lead us to a better understanding of QFT.

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