Related papers: Proving the AGT relation for N_f = 0,1,2 antifunda…

We show that Nekrasov instanton partition function for SU(N) gauge theories satisfies recursion relations in the form of U(1)+Virasoro constraints when {\beta} = 1. The constraints give a direct support for AGT conjecture for general quiver…

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…

We prove the connection between the Nekrasov partition function of N=2 super-symmetric U(2) gauge theory with adjoint matter and conformal blocks for the Virasoro algebra, as predicted by the Alday-Gaiotto-Tachikawa relations.…

We use AGT correspondence between N=2 SUSY Yang-Mills theory on ${\mathbb R}^4/{\mathbb Z}_2$ and two-dimensional CFT model with the algebra $ {\cal H} \oplus \hat{sl}(2)_2 \oplus \text{NSR}$ to obtain the explicit expressions for 4-point…

We study $SU(2)$ gauge theories coupled to $(A_1,D_N)$ theories with or without a fundamental hypermultiplet. For even $N$, a formula for the contribution of $(A_1,D_N)$ to the Nekrasov partition function was recently obtained by us with…

We study Nekrasov's instanton partition function of four-dimensional N=2 gauge theories in the presence of surface operators. This can be computed order by order in the instanton expansion by using results available in the mathematical…

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 N=2 super-conformal field theories in four dimensions that correspond to mass-deformed linear quivers with n gauge groups and (bi-)fundamental matter. We describe them using Seiberg-Witten curves obtained from an M-theory…

We propose a relation between correlation functions in the 2d A_{N-1} conformal Toda theories and the Nekrasov instanton partition functions in certain conformal N=2 SU(N) 4d quiver gauge theories. Our proposal generalises the recently…

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…

In these notes we consider relation between conformal blocks and the Nekrasov partition function of certain $\mathcal{N}=2$ SYM theories proposed recently by Alday, Gaiotto and Tachikawa. We concentrate on $\mathcal{N}=2^{*}$ theory, which…

AGT conjecture connects Nekrasov instanton partition function of 4D quiver gauge theory with 2D Liouville conformal blocks. We re-investigate this connection using the central extension of spherical Hecke algebra in q-coordinate…

We study the non-perturbative properties of N=2 super conformal field theories in four dimensions using localization techniques. In particular we consider SU(2) gauge theories, deformed by a generic epsilon-background, with four fundamental…

We study the equivariant instanton partition function in $\mathcal{N}=2$ supersymmetric theory on $\mathbb{C}^2$ with $SU(N)$ gauge group and find the generalisation of the Zamolodchikov recurrence relation. We consider the pure theory as…

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)…

We survey and compare recent approaches to the computation of the partition functions and correlators of chiral BPS observables in $\mathcal{N}=2$ gauge theories on ALE spaces based on quiver varieties and the minimal resolution $X_k$ of…

We construct an action of N=2 affine $A_n$ quiver gauge model having non-canonical kinetic terms and equipped with electric and magnetic FI terms. N=2 supersymmetry is shown to be broken to N=1 spontaneously and N=1 multiplets realized on…

Linear recursion relations for the instanton corrections to the effective prepotential are derived for two cases of N=2 supersymmetric gauge theories; the first case with an arbitrary number of hypermultiplets in the fundamental…

We give some evidences which imply that W(1+infinity) algebra describes the symmetry behind AGT(-W) conjecture: a correspondence between the partition function of N=2 supersymmetric quiver gauge theories and the correlators of Liouville…

We work out Seiberg-like dualities for 3d $\mathcal{N}=2$ theories with SU(N) gauge group. We use the $SL(2,\mathbb{Z})$ action on 3d conformal field theories with U(1) global symmetry. One of generator S of $SL(2,\mathbb{Z})$ acts as…