Periodic Reporting for period 4 - CurvedSusy (Dynamics of Supersymmetry in Curved Space)
Berichtszeitraum: 2019-01-01 bis 2020-08-31
Notwithstanding our ability to use Quantum Field Theories in different settings, we lack a complete understanding of their structure, and their dynamics is often mysterious. There are well-established techniques to analyse systems whose components interact weakly among themselves. In this case we can regard the interactions as small perturbations of a simple system with independent components. Many natural phenomena are however characterised by strong self-interactions (e.g. high temperature superconductors, or the forces binding nuclei) and their analysis requires going beyond perturbation theory.
The aim of this project is that of deriving new exact results in Quantum Field Theory that will be valid when perturbative techniques are not applicable. In the quest for exact results physicists are greatly helped by the presence of symmetries. This project makes use of a very special kind of these: supersymmetry. There are several reasons why supersymmetric field theories are very interesting. Firstly Nature itself could be supersymmetric, a possibility that is currently at the center of the explorations of elementary particle physics at experiments like the Large Hadron Collider. Secondly supersymmetric field theories are in many respects simpler than generic ones, and can be studied exactly even at strong coupling. Nevertheless their dynamics displays phenomena, like confinement or the breaking of chiral symmetries, that occur in Nature and are extremely difficult to study analytically.
Another question we looked at is if quantum effects can spoil supersymmetry in curved space or modify its consequences on physical observables. Ultimately if supersymmetry is spoiled by the quantum effects we analyzed one could worry that it could be impossible to reconcile it with general relativity, however we argued that this is not the case.
We also investigated the possibility that different systems can be related when placed on a curved space. For instance we showed how certain results obtained for supersymmetric field theories in five dimensions can shed light on the structure and properties of supersymmetric field theories in four dimensions. The intuition coming from five dimensions helped us in defining new supersymmetric field theories in four dimensions on curved spaces with very diverse characteristics. All these spaces do not change as they are "rotated" around. It turns out that the physical observables in these theories can be computed by looking at their behavior around those special points in space that are fixed under the rotation. The geometry of space and the properties of physical observables in these theories are deeply intertwined and studying one can shed new light on the other.
Finally we showed how quantum field theoretical techniques can be used to understand the dynamics of massive bodies interacting gravitationally. This had direct implications for the computation of the properties of the gravitational radiation emitted by black hole mergers which is now accessible to observations using interferometers.
The research outcomes we obtained have opened several enticing avenues for further research that we plan to continue exploring in the future. Possible applications range from the analysis of quantum field theories at strong coupling to the computation of properties of black holes and their interactions.
The results of this project have been reported in peer-reviewed international journals and members of the research team have disseminated them at workshops and conferences.
We also paved the way to extending the use of supersymmetry to non-relativistic systems with potential applications to the study of the properties of matter at low energies.