Related papers: Trinion Conformal Blocks from Topological strings

General properties of perturbed conformal field theory interacting with quantized Liouville gravity are considered in the simplest case of spherical topology. We discuss both short distance and large distance asymptotic of the partition…

Following a recent paper by Alday and Tachikawa, we compute the instanton partition function in the presence of the surface operator by the localization formula on the moduli space. For SU(2) theories we find an exact agreement with CFT…

We consider the problem of computing (irregular) conformal blocks in 2d CFTs whose chiral symmetry algebra is the N=2 superconformal algebra. Our construction uses two ingredients: (i) the relation between the representation theories of the…

We compute the conformal blocks associated with scalar-scalar-fermion-fermion 4-point functions in 3D CFTs. Together with the known scalar conformal blocks, our result completes the task of determining the so-called `seed blocks' in three…

Based on our generalization of the Goulian-Li continuation in the power of the 2D cosmological term we construct the two and three-point correlation functions for Liouville exponentials with generic real coefficients. As a strong argument…

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 provide evidence that the conformal blocks of N=1 super Liouville conformal field theory are described in terms of the SU(2) Nekrasov partition function on the ALE space O_{P^1}(-2).

We consider a generalization of the two-dimensional Liouville conformal field theory to any number of even dimensions. The theories consist of a log-correlated scalar field with a background $\mathcal{Q}$-curvature charge and an exponential…

We consider the long-standing problem of obtaining the 3-point functions of Toda CFT. Our main tools are topological strings and the AGT-W relation between gauge theories and 2D CFTs. In arXiv:1310.3841 we computed the partition function of…

The continuation of the Liouville conformal field theory to c<=1 is considered. The viability of an interpretation involving a timelike boson which is the conformal factor for two-dimensional asymptotically de Sitter geometries is examined.…

We study the partition function of type IIA string theory on 10-manifolds of the form T^2 x X where X is 8-dimensional, compact, and spin. We pay particular attention to the effects of the topological phases in the supergravity action…

Three-point correlation function in perturbed conformal field theory coupled to two-dimensional quantum gravity (perturbed Liouville gravity) is explicitly computed by using the free field approach. The representation considered here is the…

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…

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…

This paper is the first part of the proof of the conformal bootstrap for Liouville conformal field theory on surfaces with a boundary, devoted to Segal's axioms in this context. We introduce the notion of Segal's amplitudes on surfaces with…

In this dissertation we present some basic features about Liouville and $\mathcal{N}=1$ Super Liouville Theory, and focus in the computation of their three point functions. Additionally, we include an introduction to Conformal Field…

We construct the four-point correlation functions containing the top component of the supermultiplet in the Neveu-Schwarz sector of the N=1 SUSY Liouville field theory. The construction is based on the recursive representation for the NS…

We study the correspondence between four-dimensional supersymmetric gauge theories and two-dimensional conformal field theories in the case of N=2* gauge theory. We emphasize the genus expansion on the gauge theory side, as obtained via…

This is the 13th article in the collection of reviews "Exact results in N=2 supersymmetric gauge theories", ed. J. Teschner. It discusses the relation between the instanton partition functions and the partition function of the topological…

All types of 4-point spheric conformal blocks in both sectors of N=1 superconformal field theory are introduced and analyzed. The elliptic recurrence formulae are derived for all the types of blocks not previously discussed in the…