Related papers: Probabilistic interpretation of quantum field theo…
In recent years, a surprisingly direct and simple rigorous understanding of quantum Liouville theory has developed. We aim here to make this material more accessible to physicists working on quantum field theory.
In the paper, we review the recent construction of the Liouville conformal field theory (CFT) from probabilistic methods, and the formalization of the conformal bootstrap. This model has offered a fruitful playground to unify the…
Originating in theoretical physics, Liouville quantum gravity (LQG) has been an important topic in probability theory and mathematical physics in the past two decades. In this proceeding, we review two aspects of this topic. The first is…
We try to develop a coherent picture on Liouville theory as a two-dimensional conformal field theory that takes into account the perspectives of path-integral approach, bootstrap, canonical quantization and operator approach. To do this, we…
Over fourty years ago, the physicist Polyakov proposed a bold framework for string theory, in which the problem was reduced to the study of certain "random surfaces". He further made the tantalising suggestion that this theory could be…
These lectures give an introduction to a probabilistic approach to Liouville Quantum Field Theory developed in a joint work with F. David, R. Rhodes and V. Vargas.
The aim of this note is to propose an interpretation for the full (non-chiral) correlation functions of the Liouville conformal field theory within the context of the quantization of spaces of Riemann surfaces.
Over the past twenty years, the probabilistic approach to Liouville Conformal Field Theory (LCFT) has undergone remarkable developments, transforming a collection of ideas at the interface of probability, geometry, complex analysis and…
A comprehensive introduction to two-dimensional conformal field theory is given.
The conformal bootstrap hypothesis is a powerful idea in theoretical physics which has led to spectacular predictions in the context of critical phenomena. It postulates an explicit expression for the correlation functions of a conformal…
We review conformal field theory on the plane in the conformal bootstrap approach. We introduce the main ideas of the bootstrap approach to quantum field theory, and how they apply to two-dimensional theories with local conformal symmetry.…
Initiated by Polyakov in his 1981 seminal work, the study of two-dimensional Liouville Conformal Field Theory has drawn considerable attention over the past decades. Recent progress in the understanding of conformal geometry in dimension…
In these mostly expository lectures, we give an elementary introduction to conformal field theory in the context of probability theory and complex analysis. We consider statistical fields, and define Ward functionals in terms of their Lie…
N=1 super Liouville field theory is one of the simplest non-rational conformal field theories. It possesses various important extensions and interesting applications, e.g. to the AGT relation with 4D gauge theory or the construction of the…
Using probabilistic methods, we first define Liouville quantum field theory on Riemann surfaces of genus $\mathbf{g}\geq 2$ and show that it is a conformal field theory. We use the partition function of Liouville quantum field theory to…
Conformal quantum field theory is reviewed in the perspective of Axiomatic, notably Algebraic QFT. This theory is particularly developped in two spacetime dimensions, where many rigorous constructions are possible, as well as some complete…
We consider a generalization of the two-dimensional Liouville conformal field theory to any number of even dimensions. The theories consist of a log-correlated scalar field with a background $\mathcal{Q}$-curvature charge and an exponential…
We construct Euclidean Liouville conformal field theories in odd number of dimensions. The theories are nonlocal and non-unitary with a log-correlated Liouville field, a ${\cal Q}$-curvature background, and an exponential Liouville-type…
We provide a brief but self-contained review of two-dimensional conformal field theory, from the basic principles to some of the simplest models. From the representations of the Virasoro algebra on the one hand, and the state-field…
Suggestions concerning the generalization of the geometric quantization to the case of nonlinear field theories are given. Results for the Liouville field theory are presented.