DYNAMICS OF SUSPERSYMMETRY IN CURVED SPACE

Physics encompasses the quantitative study of Nature from the largest scales, embracing the entire observable Universe, to the tiny distances between the fundamental constituents of matter that are accessible by accelerator experiments like the Large Hadron Collider. One of the main tools we have at our disposal to understand Nature is Quantum Field Theory (QFT), a unified theory of many body systems in the Quantum regime. It is remarkable that QFT can be used to describe quantitatively phenomena as diverse as elementary particle interactions at collider experiments, the state of condensed matter systems, and the fluctuations in the cosmic microwave background. Together with General Relativity, Quantum Field Theory is the framework physicists have used to understand Nature for most of the last century.
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.