Related papers: Finite $\epsilon_2$-corrections to the $\mathcal{N…
We provide a description of the quantum integrable structure behind the Thermodynamic Bethe Ansatz (TBA)-like equation derived by Nekrasov and Shatashvili (NS) for $\mathcal{N}=2$ 4d Super Yang-Mills (SYM) theories. In this regime of the…
The Mayer cluster expansion technique is applied to the Nekrasov instanton partition function of $\mathcal{N}=2$ $SU(N_c)$ super Yang-Mills. The subleading small $\epsilon_2$-correction to the Nekrasov-Shatashvili limiting value of the…
In this work we study the Nekrasov-Shatashvili limit of the Nekrasov instanton partition function of Yang-Mills field theories with N=2 supersymmetry and gauge group SU(n). The theories are coupled with fundamental matter. The equation that…
In this work we study the Nekrasov--Shatashvili limit of the Nekrasov instanton partition function of Yang--Mills field theories with ${\cal N}=2$ supersymmetry and gauge group SU(N). The theories are coupled with fundamental matter. A path…
We study the thermodynamic behaviour of the real $\beta$- and $\gamma_i$-deformation of $\mathcal{N}=4$ Super Yang-Mills theory on $\mathbb{R}\times S^3$ in the planar limit. These theories were shown to be the most general asymptotically…
We study the multi-instanton partition functions of the $\Omega$-deformed $\mathcal N =2^{*}$ $SU(2) $ gauge theory in the Nekrasov-Shatashvili (NS) limit. They depend on the deformation parameters $\epsilon_{1}$, the scalar field…
We examine the two-dimensional U(N) Yang-Mills theory by using the technique of random partitions. We show that the large N limit of the partition function of the 2D Yang-Mills theory on S^2 reproduces the instanton counting of 4D N=2…
The scaling dimensions of large operators in N=4 supersymmetric Yang-Mills theory are dual to energies of semiclassical strings in AdS(5)xS(5). At one loop, the dimensions of large operators can be computed with the help of Bethe ansatz and…
We apply exact WKB methods to the study of the partition function of pure N=2 epsilon_i-deformed gauge theory in four dimensions in the context of the 2d/4d correspondence. We study the partition function at leading order in…
We study Nekrasov's deformed partition function of 5-dimensional supersymmetric Yang-Mills theory compactified on a circle. Mathematically it is the generating function of the characters of the coordinate rings of the moduli spaces of…
We give a mathematically rigorous proof of Nekrasov's conjecture: the integration in the equivariant cohomology over the moduli spaces of instantons on $\mathbb R^4$ gives a deformation of the Seiberg-Witten prepotential for N=2 SUSY…
We compute $e^{-AN}$ corrections to the Gross-Taylor 1/N expansion of the paritition function of two-dimensional SU(N) and U(N) Yang Mills theory. We find a very similar structure of mixing between holomorphic and anti-holomorphic sectors…
We study N=2 super Yang-Mills theory with gauge group SU(N) from the point of view of the Whitham hierarchy. We develop a new recursive method to compute the whole instanton expansion of the prepotential using the theta function associated…
We consider non-planar one-loop anomalous dimensions in maximally supersymmetric Yang-Mills theory and its marginally deformed analogues. Using the basis of Bethe states, we compute matrix elements of the dilatation operator and find…
We extend the graviphoton-corrected prepotential of five-dimensional pure U(N) super Yang-Mills, which was originally proposed by Nekrasov, by incorporating the effect of the five-dimensional Chern-Simons term. This extension allows us to…
In this paper, we examine scaling dimensions at small spin in the so-called sl(2) sector of the planar maximally supersymmetric Yang-Mills theory. We find that the Bethe ansatz equations, which control the spectrum of scaling dimensions,…
We give an explicit derivation of the Picard-Fuchs equations for N=2 supersymmetric SU(3) Yang-Mills theory with $N_f<6$ massive hypermultiplets in the fundamental representation. We determine the instanton corrections to the prepotential…
We review recent work on the study of N=2 super Yang-Mills theory with gauge group SU(N) from the point of view of the Whitham hierarchy, mainly focusing on three main results: (i) We develop a new recursive method to compute the whole…
We perform direct diagrammatic calculations of the anomalous dimensions of twist-two operators in extended N=2 and N=4 super Yang-Mills theories (SYM). In the case of N=4 SYM, we compute the four-loop anomalous dimension of the twist-two…
We develop a novel bi-harmonic $\mathcal{N}=4$ superspace formulation of the $\mathcal{N}=4$ supersymmetric Yang-Mills theory (SYM) in four dimensions. In this approach, the $\mathcal{N}=4$ SYM superfield constraints are solved in terms of…