Report
Teaser, summary, work performed and final results
Periodic Reporting for period 3 - CurvedSusy (Dynamics of Supersymmetry in Curved Space)
Teaser
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...
Summary
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.
Work performed
The main idea we have used to analyse strongly coupled supersymmetric theories is to place them in curved space. The intuition behind this approach is that by studying how simple observable quantities depend on the geometry of space-time we gain new insight in the dynamical properties of the theories under consideration. For instance we considered systems that can be analysed perturbatively when put in a small space but where non-perturbative effects become important as space-time gets larger. Knowing precisely the dependence on the size of space of certain supersymmetric quantities we can therefore compute them perturbatively at small distances and use them to understand properties of the non-perturbative system at large distances.
We also looked at 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.
Final results
The results we obtained so far apply to situations with a lot of symmetries. Hence it will be important to establish ways to use them as a guide to understand the dynamics of more generic physical systems.
Another line of investigation would be that of extending the use of supersymmetry to non-relativistic systems with potential applications to the study of the properties of matter at low energies.
The ultimate goal of the project is to provide new tools to study the dynamical properties of quantum systems at strong coupling. These will enhance our knowledge of quantum field theory and help us in our quest to understand many physical phenomena. Additionally this program will explore new connections between Physics and Mathematics. Historically, such relations have been extremely fruitful in the developments of both subjects.