Related papers: Instantons and the 5D U(1) gauge theory with extra…
In this thesis we discuss non-perturbative phenomena emerging in gauge and in string/supergravity theories. We compute the partition function of 5D minimal supersymmetric U(1) gauge theory with extra adjoint matter in general…
We study the partition function of the compactified 5D U(1) gauge theory (in the Omega-background) with a single adjoint hypermultiplet, calculated using the refined topological vertex. We show that this partition function is an example a…
We present the unrefined instanton partition functions of various 5d gauge theories with matter beyond the fundamental representation as sums over Young diagrams. By using these explicit expressions, we verify a range of identities among…
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 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 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…
We refine a previous proposal for obtaining the multi-instanton partition function from the supersymmetric index of the 1d supersymmetric gauge theory on the worldline of D0-branes. We provide examples where the refinements are crucial for…
The superconformal index for N=2 5d theories contains a non-perturbative part arising from 5d instantonic operators which coincides with the Nekrasov instanton partition function. In this note, for pure gauge theories, we elaborate on the…
We propose a set of novel expansions of Nekrasov's instanton partition functions. Focusing on 5d supersymmetric pure Yang-Mills theory with unitary gauge group on $\mathbb{C}^2_{q,t^{-1}} \times \mathbb{S}^1$, we show that the instanton…
We consider $\mathcal{N}=2$ supersymmetric pure gauge theories on toric K\"ahler manifolds, with particular emphasis on $\mathbb{CP}^2$. By choosing a vector generating a $U(1)$ action inside the torus of the manifold, we construct…
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…
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…
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 extend the instanton calculus for N=1/2 U(2) supersymmetric gauge theory by including one massless flavor. We write the equations of motion at leading order in the coupling constant and we solve them exactly in the non(anti)commutativity…
The circle compactification of the 6-dim (2,0) superconformal theory of $A_{N-1}$ type leads the 5-dim SU(N) maximally supersymmetric gauge theory. Instanton solitons embody Kaluza-Klein modes and are conjectured to be composed of partonic…
Using D3/D(-1) brane set-up in type IIB string theory we introduce gauge-stringy instantons in N=2 U(N) supersymmetry theories with one matter multiplet in symmetric representation. In addition to the gauge and stringy moduli there exist…
We calculate the partition functions of supersymmetric gauge theories on S^5, which acquire non-perturbative contributions from instanton loops wrapping its Hopf fiber. The instantons on the CP^2 base equivariantly localize to 3 fixed…
The arcane ADHM construction of Yang-Mills instantons can be very naturally understood in the framework of D-brane dynamics in string theory. In this point-of-view, the mysterious auxiliary symmetry of the ADHM construction arises as a…
Non-singular instantons are shown to exist on noncommutative R^4 even with a U(1) gauge group. Their existence is primarily due to the noncommutativity of the space. The relation between U(1) instantons on noncommutative R^4 and the…
We study the stringy instanton partition function of four dimensional ${\cal N}=2$ $U(N)$ supersymmetric gauge theory which was obtained by Bonelli et al in 2013. In type IIB string theory on $\mathbb{C}^2\times T^*\mathbb{P}^1\times…