Related papers: Conformal blocks as Dotsenko-Fateev Integral Discr…
Once famous and a little mysterious, AGT relations between Nekrasov functions and conformal blocks are now understood as the Hubbard-Stratanovich duality in the Dijkgraaf-Vafa (DV) phase of a peculiar Dotsenko-Fateev multi-logarithmic…
We study the solution of the Schlesinger system for the 4-point $\mathfrak{sl}_N$ isomonodromy problem and conjecture an expression for the isomonodromic $\tau$-function in terms of 2d conformal field theory beyond the known $N=2$…
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)…
Based on our earlier work on free field realizations of conformal blocks for conformal field theories with $SL(2)$ current algebra and with fractional level and spins, we discuss in some detail the fusion rules which arise. By a careful…
We study four-point correlation functions of four generic half-BPS supermultiplets of N=4 SCFT in four dimensions. We use the two-particle Casimir of four-dimensional superconformal algebra to derive superconformal blocks which contribute…
The characteristic multi-dimensional integrals that represent physical quantities in random-matrix models, when calculated within the supersymmetry method, can be related to a class of integrals introduced in the context of two-dimensional…
In this note we demonstrate that, as we conjectured earlier in [1], the a-charge in the conformal anomaly in dimension $d=2n$ manifests in a $n$-point correlation function of energy momentum tensor of a CFT considered in flat spacetime with…
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…
We observe that conformal blocks of scalar 4-point functions in a $d$-dimensional conformal field theory can mapped to eigenfunctions of a 2-particle hyperbolic Calogero-Sutherland Hamiltonian. The latter describes two coupled…
Conformal blocks for correlation functions of tensor operators play an increasingly important role for the conformal bootstrap programme. We develop a universal approach to such spinning blocks through the harmonic analysis of certain…
We consider the AGT relation, expressing conformal blocks for the Virasoro and W-algebras in terms of Nekrasov's special functions, in the simplest case of the 4-point functions for the first non-trivial W_3 algebra. The standard set of…
We continue to investigate the dual description of the Virasoro conformal blocks arising in the framework of the classical limit of the AdS$_3$/CFT$_2$ correspondence. To give such an interpretation in previous studies, certain restrictions…
We uncover a striking connection between conformal blocks and fractional calculus. By employing a modified form of half-derivates, we derived explicitly the exact form of the three-dimensional conformal block, expressed as the product of…
We continue our study of the semi-classical (large central charge) expansion of the toroidal one-point conformal block in the context of the 2d/4d correspondence. We demonstrate that the Seiberg-Witten curve and (epsilon1-deformed)…
The conformal invariance properties of the QCD Pomeron in the transverse plane allow us to give an explicit analytical expression for the conformal eigenvectors in the mixed representation in terms of two conformal blocks, each block being…
In recent work, Damiolini-Gibney-Tarasca showed that for a $C_2$-cofinite rational CFT-type vertex operator algebra $\mathbb V$, sheaves of conformal blocks are locally free and satisfy the factorization property. In this article, we use…
We uncover a precise relation between superblocks for correlators of superconformal field theories (SCFTs) in various dimensions and symmetric functions related to the $BC$ root system. The theories we consider are defined by two integers…
We extend the proof from arXiv:1012.3137, which interprets the AGT relation as the Hubbard-Stratonovich duality relation to the case of 5d gauge theories. This involves an additional q-deformation. Not surprisingly, the extension turns out…
For a hypersurface V of a conformal space, we introduce a conformal differential invariant I = h^2/g, where g and h are the first and the second fundamental forms of V connected by the apolarity condition. This invariant is called the…
We show that conformal blocks simplify greatly when there is a large difference between two of the scaling dimensions for external operators. In particular the spacetime dimension only appears in an overall constant which we determine via…