Related papers: A note on the Virasoro blocks at order $1/c$
We formulate a set of general rules for computing $d$-dimensional four-point global conformal blocks of operators in arbitrary Lorentz representations in the context of the embedding space operator product expansion formalism…
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…
We introduce a large class of conformally-covariant differential operators and a crossing equation that they obey. Together, these tools dramatically simplify calculations involving operators with spin in conformal field theories. As an…
The 4D 4-point scattering amplitude of massless scalars via a massive exchange is expressed in a basis of conformal primary particle wavefunctions. This celestial amplitude is expanded in a basis of 2D conformal partial waves on the unitary…
We extend Felder's construction of Fock space resolutions for the Virasoro minimal models to all irreducible modules with $c\leq 1$. In particular, we provide resolutions for the representations corresponding to the boundary and exterior of…
We derive Cardy-like formulas for the growth of operators in different sectors of unitary $2$ dimensional CFT in the presence of topological defect lines by putting an upper and lower bound on the number of states with scaling dimension in…
Black hole microstates and their approximate thermodynamic properties can be studied using heavy-light correlation functions in AdS/CFT. Universal features of these correlators can be extracted from the Virasoro conformal blocks in CFT2,…
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.…
Virasoro conformal blocks are a family of important functions defined as power series via the Virasoro algebra. They are a fundamental input to the conformal bootstrap program for 2D conformal field theory (CFT) and are closely related to…
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…
In the limit of large central charge $c$ the 4-point Virasoro conformal block becomes a hypergeometric function. It is represented by a sum of chiral Nekrasov functions, which can also be explicitly evaluated. In this way the known proof of…
Virasoro conformal blocks are universal ingredients of correlation functions of two-dimensional conformal field theories (2d CFTs) with Virasoro symmetry. It is acknowledged that in the (classical) limit of large central charge of the…
We study large $c$ conformal blocks outside the known limits. This work seems to be hard, but it is possible numerically by using the Zamolodchikov recursion relation. As a result, we find new some properties of large $c$ conformal blocks…
This is the first in a series of papers on the search for the 2D CFT description of a large class of 4D $\mathcal{N} = 1$ gauge theories. Here, we identify the 2D CFT symmetry algebra and its representations, namely the conformal blocks of…
We derive new constraints on the spectrum of two-dimensional conformal field theories with central charge $c>1.$ Employing the pillow representation of the four point correlator of identical scalars with dimension $\Delta_{\mathcal{O}}$ and…
We demonstrate that any scale-invariant mechanics of one variable exhibits not only 0+1 conformal symmetry, but also the symmetries of a full Virasoro algebra. We discuss the implications for the adS/CFT correspondence.
We introduce a full set of rules to directly express all $M$-point conformal blocks in one- and two-dimensional conformal field theories, irrespective of the topology. The $M$-point conformal blocks are power series expansion in some…
Recently, with the help of Parisi-Sourlas supersymmetry an intriguing relation was found expressing the four-point scalar conformal block of a (d-2)-dimensional CFT in terms of a five-term linear combination of blocks of a d-dimensional…
We compute the contribution of the vacuum Virasoro representation to the genus-two partition function of an arbitrary CFT with central charge $c>1$. This is the perturbative pure gravity partition function in three dimensions. We employ a…
In this paper, we analyze Virasoro conformal blocks in the limit when the operator exchange dimension is taking to be large in comparison with the other parameters dependence of the block. We do this by using Zamolodchikov's recursion…