Description du projet
Des approches de résolution des théories des champs conformes à l’aide de techniques bootstrap
Une théorie des champs conforme est une théorie quantique des champs qui est invariante sous des transformations conformes. Elle est fréquemment utilisée pour décrire les points critiques des systèmes classiques et quantiques. Le projet FUNBOOTS, financé par l’UE, projette de développer un ensemble d’outils révolutionnaires – les fonctionnelles extrémales analytiques – afin d’approfondir la compréhension de ces théories. Les chercheurs auront recours au programme d’amorçage conforme, qui est une nouvelle approche de la construction et de la classification des théories des champs conformes de manière non perturbatrice. Il exploite les conditions de cohérence de base qui sont codées dans un énorme ensemble d’équations bootstrap pour cartographier et déterminer l’espace des théories des champs conformes. Les outils proposés permettront d’extraire des informations des équations bootstrap.
Objectif
Conformal Field Theories (CFTs) have a wide range of experimental and theoretical applications: describing classical and
quantum critical phenomena, where they determine critical exponents; as low (or high) energy limits of ordinary quantum
field theories; and as theories of quantum gravity in disguise via the AdS/CFT correspondence.
Unfortunately, most interesting CFTs are strongly interacting and difficult to analyse. On the one hand, perturbative and
renormalization group methods usually involve approximations that are hard to control and which require difficult
resummations. On the other hand, numerical simulations of the underlying systems are difficult near the critical point and can
access only a limited set of observables.
The conformal bootstrap program is a new approach. It exploits basic consistency conditions which are encoded into a
formidable set of bootstrap equations, to map out and determine the space of CFTs. A longstanding conjecture states that
these equations actually provide a fully non-perturbative definition of CFTs. In this project we will develop a groundbreaking
set of tools ? analytic extremal functionals ? to extract information from the bootstrap equations. This Functional Bootstrap
has the potential to greatly deepen our understanding of CFTs as well as to determine incredibly precise bounds on the
space of theories. Our main goals are A) to fully develop the functional bootstrap for the simpler and mostly unexplored one-
dimensional setting, relevant for critical systems such as spin models with long-range interactions and line defects in
conformal gauge theories, leading to analytic insights and effective numerical solutions of these systems; and B) to establish
functionals as the default technique for higher dimensional applications by developing the formalism, obtaining general
analytic bounds and integrating into existing numerical workflows to obtain highly accurate determinations of critical
exponents
Champ scientifique
Mots‑clés
Programme(s)
- HORIZON.1.1 - European Research Council (ERC) Main Programme
Régime de financement
HORIZON-ERC - HORIZON ERC GrantsInstitution d’accueil
75794 Paris
France