Related papers: Proving AGT relations in the large-c limit
The recent AGT suggestion to use the set of Nekrasov functions as a basis for a linear decomposition of generic conformal blocks works very well not only in the case of Virasoro symmetry, but also for conformal theories with extended chiral…
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…
The Seiberg-Witten prepotentials for N=2 SUSY gauge theories with N_f<2N_c fundamental multiplets are obtained from conformal N_f=2N_c theory by decoupling 2N_c-N_f multiplets of heavy matter. This procedure can be lifted to the level of…
Given a 4d N=2 SUSY gauge theory, one can construct the Seiberg-Witten prepotentional, which involves a sum over instantons. Integrals over instanton moduli spaces require regularisation. For UV-finite theories the AGT conjecture favours…
The AGT conjecture identifying conformal blocks with the Nekrasov functions is investigated for the spherical conformal blocks with more than 4 external legs. The diagram technique which arises in conformal block calculation involves…
Virasoro conformal blocks are fixed in principle by symmetry, but a closed-form expression is unknown in the general case. In this work, we provide three closed-form expansions for the four-point Virasoro blocks on the sphere, for arbitrary…
AGT allows one to compute conformal blocks of d = 2 CFT for a large class of chiral CFT algebras. This is related to the existence of a certain orthogonal basis in the module of the (extended) chiral algebra. The elements of the basis are…
Based on prototypical example of Al.Zamolodchikov's recursion relations for the four point conformal block and using recently proposed Alday-Gaiotto-Tachikawa (AGT) conjecture, recursion relations are derived for the generalized…
We consider the semiclassical limit of the vacuum Virasoro block describing the diagonal 4-point correlation functions on the sphere. At large central charge c, after exponentiation, it depends on two fixed ratios h_H/c and h_L/c, where…
Recently, an intriguing family of the one-point toric conformal blocks AGT related to the $\mathcal{N}=2^*\,\, SU(2)$ Nekrasov functions was discovered by M. Beccaria and G. Macorini. Members of the family are distinguished by having only…
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 derive an explicit expression for the $1/c$ contribution to the Virasoro blocks in 2D CFT in the limit of large $c$ with fixed values of the operators' dimensions. We follow the direct approach of orthonormalising, at order $1/c$, the…
We analytically determine the large central charge asymptotic expansion of the Virasoro conformal blocks entering in four-point functions with external degenerate operators on a sphere in $2d$ CFTs, and study its resurgence properties as a…
In this paper, we study large $c$ Virasoro blocks by using the Zamolodchikov monodromy method beyond its known limits. We give an analytic proof of our recent conjectur, which implied that the asymptotics of the large $c$ conformal blocks…
Recursion relations for the sphere $4$-point and torus $1$-point ${\cal W}_3$ conformal blocks, generalizing Alexei Zamolodchikov's famous relation for the Virasoro conformal blocks are proposed. One of these relations is valid for any…
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…
Virasoro conformal blocks are expected to exponentiate in the limit of large central charge $c$ and large operator dimensions $h_i$, with the ratios $h_i/c$ held fixed. We prove this by employing the oscillator formulation of the Virasoro…
In their recent paper \cite{Alday:2009aq} Alday, Gaiotto and Tachikawa proposed a relation between $\mathcal{N}=2$ four-dimensional supersymmetric gauge theories and two-dimensional conformal field theories. As part of their conjecture they…
The AGT conjecture claims an equivalence of conformal blocks in 2d CFT and sums of Nekrasov functions (instantonic sums in 4d SUSY gauge theory). The conformal blocks can be presented as Dotsenko-Fateev beta-ensembles, hence, the AGT…
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…