| Summary: |
Quantum field theory (QFT) plays a pivotal role in elucidating a wide array of physical phenomena, ranging from condensed matter systems, high- energy particle collisions in accelerators, the evolution of cosmological perturbations and high precision gravitational wave physics. Moreover, it stands as a prominent candidate for the integration of quantum theory and gravity, with the gauge gravity duality serving as a notable illustration of this potential unification. Within this framework a conformal field theory (CFT) in d dimensions is dual to a quantum gravity theory living in a d+1 dimensional space in Anti-de-Sitter, this is the essence of AdS/CFT duality.
A robust mathematical framework that describes analytically physical phenomena such as confinement, chiral symmetry breaking, and the existence of a mass gap is currently lacking. Additionally, the specific field theory mechanism through which gauge/string dualities occur is not yet fully understood. Unfortunately, a considerable portion of physical systems exhibits a strongly coupled nature, eluding many conventional theoretical methods aimed at addressing these complexities or require the computation of Feynman type diagrams or integrals that are hard to harness. So to tackle these fascinating questions one needs new and powerful tools.
Fortunately, a significant amount of progress has happened during the last decades to develop and explore new non-perturbative approaches to describe quantum field theories at finite coupling and as well as new methods to exploit the perturbative regime to unprecedented levels.
The goal of this project is to take advantage, further develop and combine(whenever it is possible) these modern methods to draw some lessons that might help understand analytically some of the strongly coupled phenomena that occurs in nature. To this end the current proposal aims to study physical observables at finite coupling in non-perturbative quantum field theories. We shall use N=4 super Y  |
Summary
Quantum field theory (QFT) plays a pivotal role in elucidating a wide array of physical phenomena, ranging from condensed matter systems, high- energy particle collisions in accelerators, the evolution of cosmological perturbations and high precision gravitational wave physics. Moreover, it stands as a prominent candidate for the integration of quantum theory and gravity, with the gauge gravity duality serving as a notable illustration of this potential unification. Within this framework a conformal field theory (CFT) in d dimensions is dual to a quantum gravity theory living in a d+1 dimensional space in Anti-de-Sitter, this is the essence of AdS/CFT duality.
A robust mathematical framework that describes analytically physical phenomena such as confinement, chiral symmetry breaking, and the existence of a mass gap is currently lacking. Additionally, the specific field theory mechanism through which gauge/string dualities occur is not yet fully understood. Unfortunately, a considerable portion of physical systems exhibits a strongly coupled nature, eluding many conventional theoretical methods aimed at addressing these complexities or require the computation of Feynman type diagrams or integrals that are hard to harness. So to tackle these fascinating questions one needs new and powerful tools.
Fortunately, a significant amount of progress has happened during the last decades to develop and explore new non-perturbative approaches to describe quantum field theories at finite coupling and as well as new methods to exploit the perturbative regime to unprecedented levels.
The goal of this project is to take advantage, further develop and combine(whenever it is possible) these modern methods to draw some lessons that might help understand analytically some of the strongly coupled phenomena that occurs in nature. To this end the current proposal aims to study physical observables at finite coupling in non-perturbative quantum field theories. We shall use N=4 super Yang-Mills theory (N=4 SYM) - a supersymmetric cousin of quantum chromodynamics - as a key toy model of our analysis. As a bonus, we shall learn about quantum gravity given that N=4 SYM is the prime and most well-studied example of the AdS/CFT duality.
One of methods is based on the old idea of deriving constraints from imposing consistency conditions based on the symmetries and analytical properties of the underlying theories. This is the essence of the by now famed conformal and S-matrix bootstrap programs that take leverage of sound and well established properties of crossing symmetry, unitarity and analyticity. The scope of these methods is quite varied as they have been applied to statistical physics systems such as the Ising model, condensed matter physics as in superfluid phase transition in He4, to conformal gauge theories or pion physics. In this project we shall devote more attention to conformal bootstrap methods that rely heavily on the associativity of the OPE (crossing). More concretely, we will extend our previous analytical conformal bootstrap ideas on holographic CFTs to learn the physics of strongly coupled CFTs as well as to analyze the space of quantum gravity theories in Anti-de-Sitter space times. This will be done by: 1] focusing on observables with more than four points, which we shall denote as multipoint in this project; 2] combining modern methods for perturbative computations to help conformal bootstrap program and vice-versa.
A second method takes advantage of the existence of an underlying integrable structure that many theories have and that opens the door to explore the use of powerful integrable methods to quantum field theories. In recent years there has been new and exciting developments in the description of important physical observables such as scattering amplitudes, Wilson loops and correlation functions using integrable objects. The first two are described by an integrable form factor with a pentagonal shape while the last one is described by an hexagonal integrable form factor. More importantly, integrable methods are orthogonal to conformal bootstrap ones and thus might be used in conjunction. In fact, one of the goals of this project is to extend and develop further a new relation, derived by us using conformal bootstrap techniques, between the two integrable form factors mentioned above.
The methods listed above have been applied with astounding success over the last decade or so to several problems. However, there are still many open and interesting unanswered questions. For instance, "What is the space of physical consistent conformal field theories (CFTs) and do these give rise to theories of quantum gravity?", etc. Here, with this project, we have designed a program to attack some interesting problems in a novel and exploratory fashion. Our goal is to make use of the consistency of multi point conformal correlators. |