Related papers: Instanton counting with a surface operator and the…
We write down an explicit conjecture for the instanton partition functions in 4d N=2 SU(N) gauge theories in the presence of a certain type of surface operator. These surface operators are classified by partitions of N, and for each…
M-theoretic construction of N=2 gauge theories implies that the instanton partition function is expressed as the scalar product of coherent states (Whittaker states) in the Verma module of an appropriate two dimensional conformal field…
We study the instanton counting in four dimensional $\mathcal{N}=2$ supersymmetric gauge theories on the blow-up of $\mathbb{C}^2$: we start by formulating the instanton moduli space as a quiver variety, which we regularise by introducing…
This is the third article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J. Teschner. It is explained how to compute the instanton partition functions. The results can be written as sums over bases…
We compute the instanton partition functions of $\mathcal{N}=1$ SCFTs in class $\mathcal{S}_k$. We obtain this result via orbifolding Dp/D(p-4) brane systems and calculating the partition function of the supersymmetric gauge theory on the…
We generalize Nakajima-Yoshioka blowup equations to arbitrary gauge group with hypermultiplets in arbitrary representations. Using our blowup equations, we compute the instanton partition functions for 4d N=2 and 5d N=1 gauge theories for…
We study the super instanton solution in the gauge theory with U$(n_{+}| n_{-})$ gauge group. Based on the ADHM construction generalized to the supergroup theory, we derive the instanton partition function from the super instanton moduli…
The aim of this memoir for "Habilitation \`a Diriger des Recherches" is to present quantum geometric and algebraic aspects of supersymmetric gauge theory, which emerge from non-perturbative nature of the vacuum structure induced by…
We study instanton partition functions for N=2 superconformal Sp(1) and SO(4) gauge theories. We find that they agree with the corresponding U(2) instanton partitions functions only after a non-trivial mapping of the microscopic gauge…
We compute the instanton partition function for ${\cal N}=4$ U(N) gauge theories living on toric varieties, mainly of type $\R^4/\Gamma_{p,q}$ including $A_{p-1}$ or $O_{\PP_1}(-p)$ surfaces. The results provide microscopic formulas for the…
These notes have two parts. The first is a study of Nekrasov's deformed partition functions $Z(\ve_1,\ve_2,\vec{a};\q,\vec{\tau})$ of N=2 SUSY Yang-Mills theories, which are generating functions of the integration in the equivariant…
We describe the modern formalism, ideas and applications of the instanton calculus for gauge theories with, and without, supersymmetry. Particular emphasis is put on developing a formalism that can deal with any number of instantons. This…
We present closed-form expressions of unrefined instanton partition functions for gauge groups of type $BCD$ as sums over Young diagrams. For $\mathrm{SO}(n)$ gauge groups, we provide a fivebrane web picture of our formula based on the…
Following a recent paper by Alday and Tachikawa, we compute the instanton partition function in the presence of the surface operator by the localization formula on the moduli space. For SU(2) theories we find an exact agreement with CFT…
There have been two distinct schemes studied in the literature for instanton counting in A_{p-1} asymptotically locally Euclidean (ALE) spaces. We point out that the two schemes---namely the counting of orbifolded instantons and instanton…
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 survey recent results on quantum corrections to the hypermultiplet moduli space M in type IIA/B string theory on a compact Calabi-Yau threefold X, or, equivalently, the vector multiplet moduli space in type IIB/A on X x S^1. Our main…
We perform a study of the moduli space of framed torsion free sheaves on Hirzebruch surfaces by using localization techniques. After discussing general properties of this moduli space, we classify its fixed points under the appropriate…
We investigate the differential geometry of the moduli space of instantons on S^3 x S^1. Extending previous results, we show that a sigma-model with this target space can be expected to possess a large N=4 superconformal symmetry,…
This is the 13th article in the collection of reviews "Exact results in N=2 supersymmetric gauge theories", ed. J. Teschner. It discusses the relation between the instanton partition functions and the partition function of the topological…