V. Belavin

Super Liouville conformal blocks from N = 2 SU(2) quiver gauge theories

The conjecture about the correspondence between instanton partition functions in the N = 2 SUSY Yang-Mills theory and conformal blocks of two-dimensional conformal field theories is extended to the case of the N = 1 supersymmetric conformal blocks. We find that the necessary modification of the moduli space of instantons requires additional restriction of Z (2)-symmetry. This leads to an explicit form of the N =1 superconformal blocks in terms of Young diagrams with two sorts of cells.The conjecture about the correspondence between instanton partition functions in theN = 2 SUSY Yang-Mills theory and conformal blocks of two-dimensi onal conformal field theories is extended to the case of the N = 1 supersymmetric conformal blocks. We find that the necessary modification of the modu li space of instantons requires additional restriction of Z(2)-symmetry. This leads to an explicit form of theN = 1 superconformal blocks in terms of Young diagrams with two so rts f cells.

AGT conjecture and Integrable structure of Conformal field theory for c=1

Abstract 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 special orthogonal basis in the module of algebra A = Vir ⊗ H . The basis vectors are the eigenvectors of the infinite set of commuting integrals of motion. It was also proven that some of these vectors take form of Jack polynomials. In this note we conjecture and verify by explicit computations that in the case of the Virasoro central charge c = 1 all basis vectors are just the products of two Jack polynomials. Each of the commuting integrals of motion becomes the sum of two integrals of motion of two noninteracting Calogero models. We also show that in the case c ≠ 1 it is necessary to use two different Feigin–Fuks bosonizations of the Virasoro algebra for the construction of all basis vectors which take form of one Jack polynomial.

Instantons and 2d superconformal field theory

A recently proposed correspondence between 4-dimensional

Classical conformal blocks via AdS/CFT correspondence

\mathcal{N} = 2

Monodromic vs geodesic computation of Virasoro classical conformal blocks

SUSY SU(k) gauge theories on

Holographic interpretation of 1-point toroidal block in the semiclassical limit

{{{{\mathbb{R}^4}}} \left/ {{{\mathbb{Z}_m}}} \right.}

From global to heavy-light: 5-point conformal blocks

and SU(k) Toda-like theories with Zm parafermionic symmetry is used to construct four-point

Conformal blocks of WN minimal models and AGT correspondence

\mathcal{N} = 1

Frobenius manifolds, Integrable Hierarchies and Minimal Liouville Gravity

super Liouville conformal block, which corresponds to the particular case k = m = 2.The construction is based on the conjectural relation between moduli spaces of SU(2) instantons on

AGT, N-Burge partitions and \( {\mathcal{W}}_N \) minimal models

{{{{\mathbb{R}^4}}} \left/ {{{\mathbb{Z}_2}}} \right.}