Descripción del proyecto
Métodos para resolver teorías de campos conformes empleando técnicas de «bootstrap»
Una teoría de campo conforme es una teoría de campo cuántico que es invariante bajo transformaciones conformes. Se utiliza de forma generalizada para describir puntos críticos de sistemas clásicos y cuánticos. En el proyecto financiado con fondos europeos FUNBOOTS se prevé crear un conjunto de herramientas revolucionarias ―funcionales analíticos extremos― para profundizar la comprensión de las teorías de campos conformes. Los investigadores utilizarán el programa de «bootstrap» conforme, que es un nuevo método para construir y clasificar teorías de campos conformes de forma no perturbativa. Este aprovecha las condiciones de consistencia básicas que están codificadas en un conjunto formidable de ecuaciones de «bootstrap» para mapear y determinar el espacio de las teorías de campos conformes. Las herramientas propuestas extraerán información de las ecuaciones de «bootstrap».
Objetivo
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
Ámbito científico
Palabras clave
Programa(s)
- HORIZON.1.1 - European Research Council (ERC) Main Programme
Régimen de financiación
HORIZON-ERC - HORIZON ERC GrantsInstitución de acogida
75794 Paris
Francia