Related papers: Exact 3D Conformal Blocks from Fractional Calculus
We introduce the definition of conformable derivative on time scales and develop its calculus. Fundamental properties of the conformable derivative and integral on time scales are proved. Linear conformable differential equations with…
Irregular conformal block is a new tool to study Argyres-Douglas theory, whose irregular vector is represented as a simultaneous eigenstate of a set of positive Virasoro generators. One way to find the irregular conformal block is to use…
We study CFT2 conformal blocks on a torus and their holographic realization. The classical conformal blocks arising in the regime where conformal dimensions grow linearly with the large central charge are shown to be holographically dual to…
A general two dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Then, applying the generators of the closed subalgebra generated by $(L_{-1}, L_{0},…
We establish that all of the one- and two-dimensional global conformal blocks are, up to some choice of prefactor, free-particle wavefunctions in tensor products of AdS$_3$ or limits thereof. Our first core observation is that the six-point…
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…
We develop techniques useful for obtaining conformal blocks in embedding space. We construct a unique differential operator in embedding space and use it to construct a function that will be an important ingredient in assembling conformal…
We examine the correspondence between the conformal field theory of boundary operators and two-dimensional hyperbolic geometry. By consideration of domain boundaries in two-dimensional critical systems, and the invariance of the hyperbolic…
The aim of this paper is to generalize the notion of conformal blocks to the situation in which the Lie algebra they are attached to is not defined over a field, but depends on covering data of curves. The result will be a sheaf of…
We compute $M$-point conformal blocks with scalar external and exchange operators in the so-called comb configuration for any $M$ in any dimension $d$. Our computation involves repeated use of the operator product expansion to increase the…
We consider the problem of computing N=2 superconformal block functions. We argue that the Kazama-Suzuki coset realization of N=2 superconformal algebra in terms of the affine sl(2) algebra provides relations between N=2 and affine sl(2)…
We study conformal blocks for thermal one-point-functions on the sphere in conformal field theories of general dimension. These thermal conformal blocks satisfy second order Casimir differential equations and have integral representations…
Two-dimensional conformal field theory (CFT) can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. The construction of a…
We propose a systematic approach to constructing microscopic models with fractional excitations in three-dimensional (3D) space. Building blocks are quantum wires described by the (1+1)-dimensional conformal field theory (CFT) associated…
The numerical conformal bootstrap has become in the last 15 years an indispensable tool for studying strongly coupled CFTs in various dimensions. Here we review the main developments in the field in the last 5 years, since the appearance of…
Three-dimensional theories with cubic symmetry are studied using the machinery of the numerical conformal bootstrap. Crossing symmetry and unitarity are imposed on a set of mixed correlators, and various aspects of the parameter space are…
In this paper we develop further the relation between conformal four-point blocks involving external spinning fields and Calogero-Sutherland quantum mechanics with matrix-valued potentials. To this end, the analysis of…
We investigate the constraints of crossing symmetry on CFT correlation functions. Four point conformal blocks are naturally viewed as functions on the upper-half plane, on which crossing symmetry acts by PSL(2,Z) modular transformations.…
We study conformal blocks (the space of correlation functions) over compact Riemann surfaces associated to vertex operator algebras which are the sum of highest weight modules for the underlying Virasoro algebra. Under the fairly general…
It is known that reflection coefficients for bulk fields of a rational conformal field theory in the presence of an elementary boundary condition can be obtained as representation matrices of irreducible representations of the classifying…