Related papers: Free Field Realisations of Staggered Modules in 2D…
Given a non-semisimple automorphism $\varphi$ of a vertex algebra $V$, the fields in a $\varphi$-twisted $V$-module involve the logarithm of the formal variable, and the action of the Virasoro operator $L_0$ on such module is not…
In this article, certain indecomposable Virasoro modules are studied. Specifically, the Virasoro mode L_0 is assumed to be non-diagonalisable, possessing Jordan blocks of rank two. Moreover, the module is further assumed to have a highest…
We show how bosonic (free field) representations for so-called degenerate conformal theories are built by singular vectors in Verma modules. Based on this construction, general expressions of conformal blocks are proposed. As an example we…
We consider dS_2/CFT_1 where the asymptotic symmetry group of the de Sitter spacetime contains the Virasoro algebra. We construct representations of the Virasoro algebra realized in the Fock space of a massive scalar field in de Sitter,…
This paper is a continuation of arXiv:1405.1707. We present certain new applications and generalizations of the free field realization of the twisted Heisenberg-Virasoro algebra ${\mathcal H}$ at level zero. We find explicit formulas for…
Logarithmic conformal field theories are based on vertex algebras with non-semisimple representation categories. While examples of such theories have been known for more than 25 years, some crucial aspects of local logarithmic CFTs have…
We investigate the free fields realization of the twisted Heisenberg-Virasoro algebra $\mathcal{H}$ at level zero. We completely describe the structure of the associated Fock representations. Using vertex-algebraic methods and screening…
We investigate a class of reducible yet indecomposable modules over the $N=2$ superconformal algebras. These so-called staggered modules exhibit a non-diagonalisable action of the Virasoro mode $L_{0}$. Using recent results on the coset…
We review some aspects of the free field approach to two-dimensional conformal field theories. Specifically, we discuss the construction of free field resolutions for the integrable highest weight modules of untwisted affine Kac-Moody…
We develop the representation of free spinor fields in the bulk of Lorentzian anti-de Sitter space in terms of smeared operators in the dual conformal field theory. To do this we expand the bulk field in a complete set of normalizable…
We study a family of fermionic oscillator representations of the Virasoro algebra via 2-point-local Virasoro fields on the Fock space $\mathit{F^{\otimes \frac{1}{2}}}$ of a neutral (real) fermion. We obtain the decomposition of…
We discuss the structure of 2D conformal field theories (CFT) at central charge c=0 describing critical disordered systems, polymers and percolation. We construct a novel extension of the c=0 Virasoro algebra, characterized by a number b…
We examine two-dimensional conformal field theories (CFTs) at central charge c=0. These arise typically in the description of critical systems with quenched disorder, but also in other contexts including dilute self-avoiding polymers and…
We construct logarithmic conformal field theories starting from an ordinary conformal field theory -- with a chiral algebra C and the corresponding space of states V -- via a two-step construction: i) deforming the chiral algebra…
It is discussed how stochastic evolutions may be linked to logarithmic conformal field theory. This introduces an extension of the stochastic Loewner evolutions. Based on the existence of a logarithmic null vector in an indecomposable…
To connect conformal field theories (CFT) to probabilistic lattice models, recent works [HKV22, Ada23] have introduced a novel definition of local fields of the lattice models. Local fields in this picture are probabilistically concrete:…
The fusion rules of conformal field theories admitting an sl^(2)-symmetry at level k=-1/2 are studied. It is shown that the fusion closes on the set of irreducible highest weight modules and their images under spectral flow, but not when…
It has long been understood that non-trivial Conformal Field Theories (CFTs) with vanishing central charge ($c=0$) are logarithmic. So far however, the structure of the identity module -- the (left and right) Virasoro descendants of the…
This article aims to review a selection of central topics and examples in logarithmic conformal field theory. It begins with a pure Virasoro example, critical percolation, then continues with a detailed exposition of symplectic fermions,…
In the context of Conformal Field Theory (CFT), many results can be obtained from the representation theory of the Virasoro algebra. While the interest in Logarithmic CFTs has been growing recently, the Virasoro representations…