Related papers: Improved matrix-model calculation of the N=2 prepo…
We study the low energy effective action of the $\Omega$-deformed $\mathcal N =2^{*}$ $SU(2) $ gauge theory. It depends on the deformation parameters $\epsilon_{1},\epsilon_{2}$, the scalar field expectation value $a$, and the…
Using recently proposed soliton equations we derive a basic identity for the scaling violation of $N=2$ supersymmetric gauge theories $\sum_i a_i\partial F/\partial a_i-2F=8 \pi i b_1 u$. Here $F$ is the prepotential, $a_i$'s are the…
We relate the non-perturbative exact results in supersymmetry to perturbation theory using several different methods: instanton calculations at weak or strong coupling, a method using gaugino condensation and another method relating strong…
We review recent work on the study of N=2 super Yang-Mills theory with gauge group SU(N) from the point of view of the Whitham hierarchy, mainly focusing on three main results: (i) We develop a new recursive method to compute the whole…
We consider the multi-instanton collective coordinate integration measure in N=2 supersymmetric SU(N) gauge theory with N_F fundamental hypermultiplets. In the large-N limit, at the superconformal point where N_F=2N and all VEVs are turned…
We construct 4D $\mathcal{N}=2$ theories on an infinite family of 4D toric manifolds with the topology of connected sums of $S^2 \times S^2$. These theories are constructed through the dimensional reduction along a non-trivial $U(1)$-fiber…
By using the recursion relations found in the framework of N=2 Super Yang-Mills theory with gauge group SU(2), we reconstruct the structure of the instanton moduli space and its volume form for all winding numbers. The construction is…
We present a semiclassical calculation of instanton effects in N=4 supersymmetric Yang-Mills theory formulated on R^{3}XS^{1} and also in the N=1 theory obtained by introducing chiral multiplet masses. In the N=4 case, these instanton…
With the aim of extending the gauge theory -- matrix model connection to more general matter representations, we prove that for various two-index tensors of the classical gauge groups, the perturbative contributions to the glueball…
We discuss the non-anticommutative (N=1/2) supersymmetric U(1) gauge theory in four dimensions, including a superpotential. We perform the one-loop renormalisation of the model, including the complete set of terms necessary for…
A procedure, allowing to calculate the coefficients of the SW prepotential in the framework of the instanton calculus is presented. As a demonstration explicit calculations for 2, 3 and 4- instanton contributions are carried out.
Instanton contributions to the anomalous dimensions of gauge-invariant composite operators in the N=4 supersymmetric SU(N) Yang-Mills theory are studied in the one-instanton sector. Independent sets of scalar operators of bare dimension 2,…
We present a Maple11+GRTensorII based symbolic calculator for instanton metrics using Newman-Penrose formalism. Gravitational instantons are exact solutions of Einstein's vacuum field equations with Euclidean signature. The Newman-Penrose…
We briefly review the properties of the N=2 U(N) gauge model with/without matters. On the vacua, N=2 supersymmetry and the gauge symmetry are spontaneously broken to N=1 and a product gauge group, respectively. The masses of the…
In N=2 super Yang-Mills theory, the Matone's relation relates instanton corrections of the prepotential to instanton corrections of scalar field condensation < Tr\phi^2 >. This relation has been proved to hold for Omega deformed theories…
N=2 supersymmetric U(N) Yang-Mills theory softly broken to N=1 by the superpotential of the adjoint scalar fields is discussed from the viewpoint of the Whitham deformation theory for prepotential. With proper identification of the…
We apply equivariant integration technique, developed in the context of instanton counting, to two dimensional N=2 supersymmetric Yang-Mills models. Twisted superpotential for U(N) model is computed. Connections to the four dimensional case…
One-instanton predictions are obtained from the Seiberg-Witten curve derived from M-theory by Landsteiner and Lopez for the Coulomb branch of N=2 supersymmetric SU(N) gauge theory with a matter hypermultiplet in the antisymmetric…
We describe the properties of instantons in lattice gauge theory when the action is a fixed point action of some renormalization group transformation. We present a theoretically consistent method for measuring topological charge using an…
We show that the integral of the first Pontrjagin class is given by an integer and it is identified with instanton number of the U(n) gauge theory on noncommutative ${\bf R^4}$. Here the dimension of the vector space $V$ that appear in the…