Integrability and Conformal Symmetry in Four Dimensions


One source of inspiration to tackle the problems of modern quantum field theory comes from the so-called gauge/gravity duality. This conjectured correspondence states that certain highly symmetric quantum field theories in four dimensions have a dual description in terms of string theories. The duality is particularly tractable in the so-called planar limit where integrable structures emerge on both sides of the correspondence. This integrability realized via so-called quantum group symmetries, together with an underlying conformal symmetry, form the mathematical backbone that allows to obtain results that had been believed to be out of reach for a long time. Integrability has been known as a feature of simpler models such as Kepler’s planetary motion or two-dimensional theories for a long time. Its emergence in a four-dimensional quantum field theory, however, opens the door to completely new applications and puzzles. The above observations inspired by the gauge/gravity duality mainly apply to very symmetric versions of four-dimensional gauge theories. This class of theories describes three of the four fundamental interactions. However, recent findings also point towards the presence of unexpected structures in theories of gravity. Here, in particular the scattering matrix and its hidden symmetries are in the focus of interest.

It is the aim of this project to progress our understanding of the symmetry structures underlying modern approaches to quantum field theory and gravity. In particular, the role of conformal and Yangian quantum group symmetries in four dimensions should be put on firm grounds. This implies to understand which properties are necessary for a quantum field theory to be integrable and how integrability and conformal symmetry can be realized in four dimensions. The recent discovery of new integrable theories, which are extremely simple, shows that we are far from understanding the space of theories with these beautiful properties.
Another important pillar of the proposal is to work out the implications of these symmetries on various observables and to turn them into practical tools for their computation. In fact, the computation of many of the considered quantities is out of reach of traditional methods. Combining the new insights with the efficient toolbox of integrability should yield the innovative tools that are necessary for further progress.
Following recent findings of a conformal symmetry in graviton scattering, the implications and systematics of this unexpected structure should also be explored. In particular, it should be understood how to prove these relations at leading order and whether they can be extended to perturbative corrections of scattering amplitudes. More generally, the role of conformal symmetry for the S-matrix of quantum gauge theories should be better understood and exploited as a computational tool.

Principal Investigators
Löbbert, Florian (Details) (Theoretical Physics / Quantum Field Theory beyond the Standard Model and String Theory)

Duration of Project
Start date: 10/2019
End date: 09/2021

Research Areas
Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields

Last updated on 2021-04-01 at 17:49