Related papers: Corrections of an elliptic block in the NS sector

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…

The structure of the 4-point N=1 super-conformal blocks in the Ramond sector is analyzed. The elliptic recursion relations for these blocks are derived.

A four point function of basic Neveu-Schwarz exponential fields is constructed in the N = 1 supersymmetric Liouville field theory. Although the basic NS structure constants were known previously, we present a new derivation, based on a…

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…

The symmetry algebra of $N=1$ Super-Liouville field theory in two dimensions is the infinite dimensional $N=1$ superconformal algebra, which allows one to prove, that correlation functions, containing degenerated fields obey some partial…

We study 2d N=4 superconformal field theories, focusing on its application on numerical bootstrap study. We derive the superconformal block by utilizing the global part of the super Virasoro algebra and set up the crossing equations for the…

In this paper, exact one-point functions of N=1 super-Liouville field theory in two-dimensional space-time with appropriate boundary conditions are presented. Exact results are derived both for the theory defined on a pseudosphere with…

A recently proposed correspondence between 4-dimensional N=2 SUSY SU(k) gauge theories on R^4/Z_m and SU(k) Toda-like theories with Z_m parafermionic symmetry is used to construct four-point N=1 super Liouville conformal block, which…

Liouville field theory on a sphere is considered. We explicitly derive a differential equation for four-point correlation functions with one degenerate field $V_{-\frac{mb}{2}}$. We introduce and study also a class of four-point conformal…

We apply an integral transformation to solutions of a partial differential equation for five-point correlation functions in Liouville theory on a sphere with one degenerate field $V_{-\frac{1}{2b}}$. By repeating this transformation, we can…

In critical loop models, there exist diagonal fields with arbitrary conformal dimensions, whose $3$-point functions coincide with those of Liouville theory at $c\leq 1$. We study their $N$-point functions, which depend on the $2^{N-1}$…

This paper focuses on the analysis of $4d$ $\mathcal{N}=4$ superconformal theories in the presence of a defect from the point of view of the conformal bootstrap. We will concentrate first on the case of codimension one, where the defect is…

We extend the work of [4] to support the conjecture that any conformal field theory with a large N expansion and a large gap in the spectrum of anomalous dimensions has a local bulk dual. We count to O(1/N^2) the solutions to the crossing…

In this paper we calculate matrix of modular transformations of the one-point toric conformal blocks in the Neveu-Schwarz sector of $N=1$ super Liouville field theory. For this purpose we use explicit expression for this matrix as integral…

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 derive one-point functions of the N=2 super-Liouville theory on a half line using the modular transformations of the characters in terms of the bulk and boundary cosmological constants. We also show that these results are consistent with…

We compute the 4d superconformal index for N=1,2 gauge theories on S^1 x L(p,1), where L(p,1) is a lens space. We find that the 4d N=1,2 index on S^1 x L(p,1) reduces to a 3d N=2,4 index on S^1 x S^2 in the large p limit, and to a 3d…

We consider the 2D super Liouville gravity coupled to the minimal superconformal theory. We analyze the physical states in the theory and give the general form of the n-point correlation numbers on the sphere in terms of integrals over the…

We use supershadow methods to derive new expressions for superconformal blocks in 4d $\mathcal{N}=1$ superconformal field theories. We analyze the four-point function $\langle\mathcal{A}_1 \mathcal{A}_2^\dagger \mathcal{B}_1…

Recently, the conformal-bootstrap has been successfully used to obtain generic bounds on the spectrum and OPE coefficients of unitary conformal field theories. In practice, these bounds are obtained by assuming the existence of a scalar…