Related papers: Partition function of N=2* SYM on a large four-sph…
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 provide a formula for the partition function of five-dimensional $\mathcal{N}=1$ gauge theories on $\mathcal{M}_4 \times S^1$, topologically twisted along $\mathcal{M}_4$ in the presence of general background magnetic fluxes, where…
N=2 supersymmetric Yang-Mills theories for all classical gauge groups, that is, for SU(N), SO(N), and Sp(N) is considered. The equations which define the Seiberg-Witten curve are proposed. In some cases they are solved. It is shown that for…
In a certain (non-commutative) version of large-N SU(N) Yang-Mills theory there are special Wilson loops, called twistor Wilson loops for geometrical reasons, whose v.e.v. is independent on the parameter that occurs in their operator…
We consider N=3 supersymmetric Chern-Simons (CS) theories that contain product U(N) gauge groups and bifundamental matter fields. Using the matrix model of Kapustin, Willett and Yaakov, we examine the Euclidean partition function of these…
We give a physical interpretation for the analytic continuation of the partition function of superconformal SU$(2)$ $\mathcal{N}=2$ gauge theory on the four-sphere to all values of the Yang-Mills coupling. We show that a well-motivated 2d…
In this paper, we study the theories with SU(2|4) symmetry which consist of the plane wave matrix model (PWMM), super Yang-Mills theory (SYM) on RxS^2 and SYM on RxS^3/Z_k. The last two theories can be realized as theories around particular…
We prove conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators in the N=4 supersymmetric Yang-Mills theory with a Gaussian matrix model. We also compute the partition…
We consider the N=4 SU(N) Super Yang Mills theory on the Coulomb branch with gauge symmetry broken to S(U(N_1) x U(N_2)). By integrating the W particles, the effective action near the IR SU(N_i) conformal fixed points is seen to be a…
We use supersymmetric localization to compute the partition function of N=2 super-Yang-Mills on S^4 in the presence of a gauged linear sigma model surface defect on a S^2 subspace. The result takes the form of a standard partition function…
Large $N$ two-dimensional QCD on a cylinder and on a vertex manifold (a sphere with three holes) is investigated. The relation between the saddle-point description and the collective field theory of QCD$_2$ is established. Using this…
We study N=4 supersymmetric Yang-Mills (SYM) theory with gauge group SU(2) compactified to three dimensions on a circle of circumference beta. The eight fermion terms in the effective action on the Coulomb branch are determined exactly, for…
We derive exact formulae for the partition function and the expectation values of Wilson/'t Hooft loops, thus directly checking their S-duality transformations. We focus on a special class of N=2 gauge theories on S^4 with fundamental…
We compute $1/\lambda$ corrections to the four-point functions of half-BPS operators in $SU(N)$ $\mathcal{N}=4$ super-Yang-Mills theory at large $N$ and large 't Hooft coupling $\lambda=g_\text{YM}^2 N$ using two methods. Firstly, we relate…
We study resurgence in the context of the partition function of 2-dimensional $SU(N)$ and $U(N)$ Yang-Mills theory on a surface of genus $h$. After discussing the properties of the transseries in the undeformed theory, we add a term to the…
An exact superpotential is derived for the N=1 theories which arise as massive deformations of N=4 supersymmetric Yang-Mills (SYM) theory. The superpotential of the SU(N) theory formulated on R^{3}\times S^{1} is shown to coincide with the…
We consider the partition function for Euclidean $SU(N)$ super Yang-Mills on a squashed seven-sphere. We show that the localization locus of the partition function has instanton membrane solutions wrapping the six "fixed" three-spheres on…
We evaluate the twisted partition function of four-dimensional $\mathcal{N} = 1$ supersymmetric Yang--Mills theory reduced to a point for all simple gauge groups. The partition function is expressed as a sum of residues. The types of…
The partition function of four dimensional Euclidean, non-supersymmetric SU(2) Yang--Mills theory is calculated in the perturbative and weak coupling regime i.e. in a small open ball about the flat connection (what we call the vicinity of…
We provide a contour integral formula for the exact partition function of ${\cal N}=2$ supersymmetric $U(N)$ gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the…