Related papers: Lectures on Instanton Counting

The AGT conjecture relates \mathcal{N}=2 4d SUSY gauge theories to 2d CFTs. Matrix model techniques can be used to investigate both sides of this relation. The large N limit refers here to the size of Young tableaux in the expression of the…

We examine the problem of counting bound states of BPS black holes on local Calabi-Yau threefolds which are fibrations over a Riemann surface by computing the partition function of q-deformed Yang-Mills theory on the Riemann surface. We…

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 construct an Imbimbo-Mukhi type matrix model, which reproduces exactly the partition function of ${\mathbb{CP}^1}$ topological strings in the small phase space, Nekrasov's instanton counting in ${\cal{N}}=2$ gauge theory and the large…

We analyze the geometric engineering of the N=2 SU(2) gauge theories with $1\leq N_f\leq 3$ massive hypermultiplets in the vector representation. The set of partial differential equations satisfied by the periods of the Seiberg-Witten…

It is well established that the spectral analysis of canonically quantized four-dimensional Seiberg-Witten curves can be systematically studied via the Nekrasov-Shatashvili functions. In this paper, we explore another aspect of the relation…

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…

In this letter we argue that instanton-dominated Green's functions in N=2 Super Yang-Mills theories can be equivalently computed either using the so-called constrained instanton method or making reference to the topological twisted version…

We propose that the structure of gauge theories, the $(2,0)$ and little-string theories is encoded in a unique function on the real group manifold $E_{10}(R)$. The function is invariant under the maximal compact subgroup $K$ acting on the…

A gauge theory can be formulated on a noncommutative (NC) spacetime. This NC gauge theory has an equivalent dual description through the so-called Seiberg-Witten (SW) map in terms of an ordinary gauge theory on a commutative spacetime. We…

We study the instanton partition functions of 5d maximal super Yang-Mills theories with all classical gauge groups. They are computed from the ADHM quantum mechanics of the D0-D4-O4 systems. Our partition functions respect S-dualities of…

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 construct ${\cal N}=2$ supersymmetric Yang-Mills theory on 4D manifolds with a Killing vector field with isolated fixed points. It turns out that for every fixed point one can allocate either instanton or anti-instanton contributions to…

We study the large N expansion of the partition function of the quiver superconformal Chern-Simons theories deformed by two continuous parameters which correspond to the general R-charge assignment to the matter fields. Though the…

The fundamentals of Statistical Mechanics require a fresh definition in the context of the developments in Classical Mechanics of integrable and chaotic systems. This is done with the introduction of Micro Partitions ; a union of disjoint…

We study (anti-) instantons in super Yang-Mills theories defined on a non anticommutative superspace. The instanton solution that we consider is the same as in ordinary SU(2) N=1 super Yang-Mills, but the anti-instanton receives corrections…

A system of Bethe-Ansatz type equations, which specify a unique array of Young tableau responsible for the leading contribution to the Nekrasov partition function in the $\epsilon_2\rightarrow 0$ limit is derived. It is shown that the…

We consider partition functions with insertions of surface operators of topologically twisted N=2, SU(2) supersymmetric Yang-Mills theory, or Donaldson-Witten theory for short, on a four-manifold. If the metric of the compact four-manifold…

We show how to obtain the instanton partition function of N=2 SYM with exceptional gauge group EFG using blow-up recursion relations derived by Nakajima and Yoshioka. We compute the two instanton contribution and match it with the recent…

The prepotential in N=2 SUSY Yang-Mills theories enjoys remarkable properties. One of the most interesting is its relation to the coordinate on the quantum moduli space $u=< \tr \phi^2>$ that results into recursion equations for the…