Related papers: Instanton counting in Class $\mathcal{S}_k$

We construct new families of $\text{AdS}_2 \times S^2 \times S^2$ solutions with 4 supercharges in Type II supergravities. We show that subclasses of these solutions can be interpreted in terms of defect branes embedded in 4d $\mathcal{N} =…

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 study worldsheet instantons in holographic type IIA backgrounds directly in string theory. The first background is a dimensional reduction of AdS$_7\times S^4$ and is dual to the maximally supersymmetric Yang-Mills theory on $S^5$. The…

We consider instanton effects in a non-supersymmetric gauge theory obtained by marginal deformations of the N=4 SYM. This gauge theory is expected to be dual to type IIB string theory on the AdS_5 times deformed-S^5 background. From an…

We explore the $\mathbb{Z}_{2,3,4,6}$ S-foldings of some 5d superconformal field theories from the $(p,q)$ 5-brane web perspective. The S-folding involves both a spatial quotient and an $\mathrm{SL}(2,\mathbb{Z})$ transformation on 5-branes…

We explore two classes of 6d $\mathcal{N}=(1,0)$ little string theories obtained from type IIA/IIB NS5-branes probing $D_n$ singularities. Their tensor branches are described by effective gauge theories whose instanton solitons are…

We show that a partition function of topological twisted N=4 Yang-Mills theory is given by Seiberg-Witten invariants on a Riemannian four manifolds under the condition that the sum of Euler number and signature of the four manifolds vanish.…

We derive the partition function of 5d ${\cal N}=1$ gauge theories on the manifold $S^3_b \times \Sigma_{\frak g}$ with a partial topological twist along the Riemann surface, $\Sigma_{\frak g}$. This setup is a higher dimensional uplift of…

For a semi-simple simply connected algebraic group G we introduce certain parabolic analogues of the Nekrasov partition function (introduced by Nekrasov and studied recently by Nekrasov-Okounkov and Nakajima-Yoshioka for G=SL(n)). These…

We describe a new technique for calculating instanton effects in supersymmetric gauge theories applicable on the Higgs or Coulomb branches. In these situations the instantons are constrained and a potential is generated on the instanton…

We analyze four-dimensional (4d) $N=1$ superconformal field theories (SCFTs) obtained as deformations of 4d $N=2$ SCFTs on S-folds by tilting 7-branes. Geometric compatibility with the structures of S-folds constrains the forms of T-branes.…

We discuss some physical issues related to the K-theoretic classification of D-brane charges, putting an emphasis on the role of D-brane instantons. The relation to D-instantons provides a physical interpretation to the mathematical…

We test the AdS/CFT correspondence by computing the partition function of some $\mathcal{N}=2$ quiver Chern-Simons-matter theories on three-sphere. The M-theory backgrounds are of the Freund-Rubin type with the seven-dimensional internal…

A large family of 4d N=2 SCFT's was introduced in arXiv:1210.2886. Its elements $D_p(G)$ are labelled by a positive integer p\in N and a simply-laced Lie group G; their flavor symmetry is at least G. In the present paper we study their…

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…

Microscopic tests of the exact results are performed in $N=2$ supersymmetric $SU(2)$ QCD. We present the complete construction of the multi-instanton in $N=2$ supersymmetric QCD. All the defining equations of the super instanton are reduced…

In the framework of the AdS/CFT duality, we calculate the supersymmetric partition function of the superconformal field theories living in the world volume of either $N$ $M2$-branes or $N$ $M5$-branes. We used the dual supergravity…

We study a system of fractional D3 and D(-1) branes in a Ramond-Ramond closed string background and show that it describes the gauge instantons of N=2 super Yang-Mills theory and their interactions with the graviphoton of N=2 supergravity.…

We present a relation between N=2 quiver gauge theories on the ALE space O_{P^1}(-2) and correlators of N=1 super Liouville conformal field theory, providing checks in the case of punctured spheres and tori. We derive a blow-up formula for…

We study the superconformal index of five-dimensional SCFTs and the sphere partition function of four-dimensional gauge theories with eight supercharges in the presence of co-dimension two half-BPS defects. We derive a prescription which is…