Related papers: Conformal Blocks for admissible representations in…
The Wakimoto construction for the quantum affine algebra U_q(\hat{sl}_2) admits a reduction to the q-deformed parafermion algebras. We interpret the latter theory as a free field realization of the Andrews-Baxter-Forrester models in regime…
We reconsider the earlier found solutions of the Knizhnik-Zamolodchikov (KZ) equations describing correlators based on the admissible representations of $A_1^{(1)}$. Exploiting a symmetry of the KZ equations we show that the original…
The representation theory of the Virasoro algebra in the case of a logarithmic conformal field theory is considered. Here, indecomposable representations have to be taken into account, which has many interesting consequences. We study the…
We study one of the simplest integrable two-dimensional quantum field theories with a boundary: $N$ free non-compact scalars in the bulk, constrained non-linearly on the boundary to lie on an $(N-1)$-sphere of radius $1/\sqrt{g}$. The $N=1$…
An explicit analytic formula is presented that computes the conformal (super-)block decomposition of any free scalar or half-BPS diagram in 1d, 2d or 4d CFTs, with various supersymmetries, including none. We prove our formula by exploiting…
Some mathematical questions relating to Coset Conformal Field Theories (CFT) are considered in the framework of Algebraic Quantum Field Theory as developed previously by us. We consider the issue of fixed point resolution in the diagonal…
We discuss some basic problems and conjectures in a program to construct general orbifold conformal field theories using the representation theory of vertex operator algebras. We first review a program to construct conformal field theories.…
We study conformal blocks of conformal field theories with a W3 symmetry algebra in the limit where the central charge is large. In this limit, we compute the four-point block as a special case of an sl3-invariant function. In the case when…
In this work we initiate an integrability-based approach to multipoint conformal blocks for higher dimensional conformal field theories. Our main observation is that conformal blocks for $N$-point functions may be considered as…
Admissible vectors lead to frames or coherent states under the action of a group by means of square integrable representations. This work shows that admissible vectors can be seen as weights with central support on the (left) group von…
Efficient methods for describing non abelian charges in worldline approaches to QFT are useful to simplify calculations and address structural properties, as for example color/kinematics relations. Here we analyze in detail a method for…
The decomposition of correlation functions into conformal blocks is an indispensable tool in conformal field theory. For spinning correlators, non-trivial tensor structures are needed to mediate between the conformal blocks, which are…
This article gives a complete account of the modular properties and Verlinde formula for conformal field theories based on the affine Kac-Moody algebra sl(2) at an arbitrary admissible level k. Starting from spectral flow and the structure…
We show how to compute conformal blocks of operators in arbitrary Lorentz representations using the formalism described in arXiv:1905.00036 and arXiv:1905.00434, and present several explicit examples of blocks derived via this method. The…
AGT correspondence gives an explicit expressions for the conformal blocks of $d=2$ conformal field theory. Recently an explanation of this representation inside the CFT framework was given through the assumption about the existence of the…
In their recent paper \cite{Alday:2009aq} Alday, Gaiotto and Tachikawa proposed a relation between $\mathcal{N}=2$ four-dimensional supersymmetric gauge theories and two-dimensional conformal field theories. As part of their conjecture they…
We derive expressions for the Virasoro OPE and four-point conformal blocks on the sphere via the resolution of identity recently determined in [Phys. Rev. D 111, 085010 (2025), arXiv:2409.12224]. Even though the resolution of the identity…
From conformal field theory on the Riemann sphere, we implement its boundary version in a simply-connected domain using the Schottky double construction. We consider the statistical fields generated by background charge modification of the…
Let $\mathbb V=\bigoplus_{n\in\mathbb N}\mathbb V(n)$ be a $C_2$-cofinite VOA, not necessarily rational or self-dual. In this paper, we establish various versions of the sewing-factorization (SF) theorems for conformal blocks associated to…
We present an analytic study of conformal field theories on the real projective space $\mathbb{RP}^d$, focusing on the two-point functions of scalar operators. Due to the partially broken conformal symmetry, these are non-trivial functions…