Related papers: Noncommutative Deformation of Instantons
We give new examples of noncommutative manifolds that are less standard than the NC-torus or Moyal deformations of $\Rb^n$. They arise naturally from basic considerations of noncommutative differential topology and have non-trivial global…
A method to construct noncommutative instantons as deformations from commutative instantons was provided in arXiv:0805.3373. Using this noncommutative deformed instanton, we investigate the spinor zero modes of the Dirac operator in a…
We show that the moduli space of the $(2,0)$ and little-string theories compactified on $T^3$ with R-symmetry twists is equal to the moduli space of U(1) instantons on a non-commutative $T^4$. The moduli space of $U(q)$ instantons on a…
We employ the twistor approach to the construction of U(2) multi-instantons `a la 't Hooft on noncommutative R^4. The noncommutative deformation of the Corrigan-Fairlie-'t Hooft-Wilczek ansatz is derived. However, naively substituting into…
{(Anti-)instanton behaviour in Euclidean non-abelian field of the point-like source is studied by analyzing the possible (anti-)instanton deformations as resulted from the variations of its characteristic parameters. The variational…
We study the notion of twisted bundles on noncommutative space. Due to the existence of projective operators in the algebra of functions on the noncommutative space, there are twisted bundles with non-constant dimension. The U(1) instanton…
We find a new gauge in which U(1) noncommutative instantons are explicitly non-singular on the whole noncommutative R^4, thus resolving the previous confusions of the author. We start with the pedagogical introduction to the noncommutative…
We present an introduction to the use of noncommutative geometry for gauge theories with emphasis on a construction of instantons for a class of four dimensional toric noncommutative manifolds. These instantons are solutions of self-duality…
We generalize the spectral-curve construction of moduli spaces of instantons on $\MT{4}$ and $K_3$ to noncommutative geometry. We argue that the spectral-curves should be constructed inside a twisted $\MT{4}$ or $K_3$ that is an elliptic…
Almost all known instanton solutions in noncommutative Yang-Mills theory have been obtained in the modified ADHM scheme. In this paper we employ two alternative methods for the construction of the self-dual U(2) BPST instanton on a…
We show that the resolution of moduli space of ideal instantons parameterizes the instantons on non-commutative $\IR^{4}$. This moduli space appears as a Higgs branch of the theory of $k$ $D0$-branes bound to $N$ $D4$-branes by the…
These notes aim at a pedagogical introduction to recent work on deformation of spaces and deformation of vector bundles over them, which are relevant both in mathematics and in physics, notably monopole and instanton bundles. We first…
IIn this article, we study the instanton equation on the cylinder over a closed manifold $X$ which admits non-zero smooth $3$-form $P$ and $4$-form $Q$. Our results are (1) if $X$ is a \textbf{good} manifold, i.e., $P,Q$ satisfying…
Recently, it was shown that in the absence of gravity there exist non-$O(4)$-symmetric instanton solutions with finite action beyond Coleman's instantons. In this paper, focusing on the false-vacuum decay in a single scalar field in flat…
We examine the dynamics of noncommutative instantons of instanton number $2$ and commutative instantons of instanton number $3$ in 5d Super Yang Mills theory. We begin by detailing the construction of the 1/4-BPS instanton solutions, their…
In noncommutative spaces, it is unknown whether the Pontrjagin class gives integer, as well as, the relation between the instanton number and Pontrjagin class is not clear. Here we define ``Instanton number'' by the size of $B_{\alpha}$ in…
We explore the deformation theory of instantons on locally conformal (LC) $Spin(7)$ manifolds. These structures, characterized by a non-parallel fundamental 4-form $\Phi$ satisfying $d\Phi = \theta \wedge \Phi$, represent a significant, yet…
Using the theory of noncommutative geometry in a braided monoidal category, we improve upon a previous construction of noncommutative families of instantons of arbitrary charge on the deformed sphere S^4_\theta. We formulate a notion of…
This is a mini-review about generalized instantons of noncommutative gauge theories in dimensions 4, 6 and 8, with emphasis on their realizations in type II string theory, their geometric interpretations, and their applications to the…
We construct a five-parameter family of gauge-nonequivalent SU(2) instantons on a noncommutative four sphere $S_\theta^4$ and of topological charge equal to -1. These instantons are critical points of a gauge functional and satisfy…