Quantum Fields at Strong Coupling, Supersymmetry and Geometry

Project title: Quantum Fields at Strong Coupling, Supersymmetry and Geometry​
Main applicant: Guido Festuccia, Division of Theoretical Physics
Grant amount: 3 560 000 SEK for the period 2019-2022
Funder: Project grant from the Swedish Research Council

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 analyze 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 characterized 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. In my project I will make 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.

The main idea we will use 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 it can happen that a system can be analysed perturbatively when it lives in a small space but that non-perturbative effects become important as space-time gets larger. If we know precisely the dependence on the size of space of a certain quantity we can therefore compute it perturbatively at small distances and use it to understand properties of the non-perturbative system at large distances. We will also look at the possibility that diverse theories can be related when placed on a curved space. The results we will obtain will be derived at first for simple theories 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.

This project will 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.