Projektbeschreibung
Ansätze zur Lösung konformer Feldtheorien mit Bootstrap-Verfahren
Eine konforme Feldtheorie ist eine Quantenfeldtheorie, die unter konformen Transformationen invariant ist. Sie wird häufig zur Beschreibung kritischer Punkte von klassischen und Quantensystemen verwendet. Das EU-finanzierte Projekt FUNBOOTS plant die Entwicklung eines bahnbrechenden Instrumentariums – analytische Extremalfunktionen –, um das Verständnis solcher Theorien zu vertiefen. Die Forschenden werden das konforme Bootstrap-Programm verwenden, einen neuen Ansatz zur nichtperturbativen Konstruktion und Klassifizierung konformer Feldtheorien. Sie nutzt grundlegende Konsistenzbedingungen, die in einem gewaltigen Satz von Bootstrap-Gleichungen kodiert sind, um den Raum der konformen Feldtheorien abzubilden und zu bestimmen. Die vorgeschlagenen Instrumente werden Informationen aus den Bootstrap-Gleichungen extrahieren.
Ziel
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
Wissenschaftliches Gebiet
Schlüsselbegriffe
Programm/Programme
- HORIZON.1.1 - European Research Council (ERC) Main Programme
Thema/Themen
Finanzierungsplan
HORIZON-ERC - HORIZON ERC GrantsGastgebende Einrichtung
75794 Paris
Frankreich