Related papers: Minimal lectures on two-dimensional conformal fiel…
We present a general study of 3-point functions of conformal field theory (CFT) in momentum space, following a reconstruction method for tensor correlators, based on the solution of the conformal Ward identities (CWIs), introduced in recent…
We study the boundary N=2 Liouville theory based on the ``modular bootstrap'' approach. As fundamental conformal blocks we introduce the ``extended characters'' that are defined as the proper sums over spectral flows of irreducible…
This is an introduction to the basic ideas and to a few further selected topics in conformal quantum field theory and in the theory of Kac-Moody algebras.
We systematically study how the integrality of the conformal characters shapes the space of fermionic rational conformal field theories in two dimensions. The integrality suggests that conformal characters on torus with a given choice of…
Higher dimensional Euclidean Liouville conformal field theories (LCFTs) consist of a log-correlated real scalar field with a background charge and an exponential potential. We analyse the LCFT on a four-dimensional manifold with a boundary.…
We construct the stress-energy tensor correlation functions in probabilistic Liouville Conformal Field Theory (LCFT) on the two-dimensional sphere by studying the variation of the LCFT correlation functions with respect to a smooth…
We introduce a method for computing conformal blocks of operators in arbitrary Lorentz representations in any spacetime dimension, making it possible to apply bootstrap techniques to operators with spin. The key idea is to implement the…
The W-infinity minimal models are conformal field theories which can describe the edge excitations of the hierarchical plateaus in the quantum Hall effect. In this paper, these models are described in very explicit terms by using a bosonic…
This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or…
We revisit the line of non-unitary theories that interpolate between the Virasoro minimal models. Numerical bootstrap applications have brought about interest in the four-point function involving the scalar primary of lowest dimension.…
We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary CFTs connecting the 2D Ising model, the 3D Ising…
In this document we prove higher equations of motion at the level 2 for boundary Liouville Conformal Field Theory. As a corollary we present a new derivation of the Belavin-Polyakov-Zamolodchikov differential equations. Our method of proof…
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…
In this paper, we elaborate on aspects of the recently introduced BMS bootstrap programme. We consider two-dimensional (2d) field theories with BMS3 symmetry and extensively use highest weight representations to uncover the BMS version of…
An analytic expression is proposed for the three-point function of the exponential fields in the Liouville field theory on a sphere. In the classical limit it coincides with what the classical Liouville theory predicts. Using this function…
We use the AdS/CFT correspondence to study flows of N=4 SYM to non-conformal theories. The dual geometries can be seen as sourced by a Wigner's semicircle distribution of D3 branes. We consider two cases, the first case corresponds to a…
We present a new framework for a Lagrangian description of conformal field theories in various dimensions based on a local version of d+2-dimensional conformal space. The results include a true gauge theory of conformal gravity in d=(1,3)…
Conformal field theories play a central role in theoretical physics with many applications ranging from condensed matter to string theory. The conformal bootstrap studies conformal field theories using mathematical consistency conditions…
Conformal field theories play a central role in modern theoretical physics with many applications to the understanding of phase transitions, gauge theories and even the quantum physics of gravity, through Maldacena's celebrated holographic…
A quantization of (2+1)-dimensional gravity with negative cosmological constant is presented and quantum aspects of the (2+1)-dimensional black holes are studied thereby. The quantization consists of two procedures. One is related with…