Related papers: Topological Charge of Noncommutative ADHM Instanto…
We have calculated the topological charge of U(N) instantons on non-degenerate noncommutative space time to be exactly the instanton number k in a previous paper [Mod.Phys.Lett. A18 1691]. This paper, which deals with the degenerate…
We study in detail the ADHM construction of U(N) instantons on noncommutative Euclidean space-time R_{NC}^4 and noncommutative space R_{NC}^2 x R^2. We point out that the completeness condition in the ADHM construction could be invalidated…
We found an exact solution of elongated U(1) instanton on noncommutative R^4 for general instanton number k. The deformed ADHM equation was solved with general k and the gauge connection and the curvature were given explicitly. We also…
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…
The ADHM constraints which implicitly specify instanton gauge field configurations are solved for the explicit general form of instantons with topological charge two and gauge group U(N).
We make some comments on noncommutative $U(N)$-instantons on $\mathbb{R}^4_{\theta}$. We elaborate on the equations for the ASD-connection for free modules. Further we make some remarks on the computation of the topological index of ADHM…
We study the U(1) and U(2) instanton solutions of gauge theory on general noncommutative $\bf{R}^4$. In all cases considered we obtain explicit results for the projection operators. In some cases we computed numerically the instanton charge…
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…
The basic objects of the ADHM construction are reformulated in terms of elements of the $A_{\theta}(R^4)$ algebra of the noncommutative $R_{\theta}^4$ space. This new formulation of the ADHM construction makes possible the explicit calculus…
We discuss the Atiyah-Drinfeld-Hitchin-Manin (ADHM) construction of U(N) instantons in noncommutative (NC) space and prove the one-to-one correspondence between moduli spaces of the noncommutative instantons and the ADHM data, together with…
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…
An alternative method to the topological instanton solution for deriving an expression for the topological charge is presented. This alternative method involves the use of relativistic quantum field theory and covariant electrodynamics. In…
We study U(1) and U(2) noncommutative instantons on R^2_{NC} x R^2_C based on the ADHM construction. It is shown that a mild singularity in the instanton solutions for both self-dual and anti-self-dual gauge fields always disappears in…
We give a \theta-deformed version of the ADHM construction of SU(2) instantons with arbitrary topological charge on the sphere S^4. Classically the instanton gauge fields are constructed from suitable monad data; we show that in 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…
We study U(1) and U(2) instanton solutions on noncommutative R^4 based on the noncommutative version of ADHM equation proposed by Nekrasov and Schwarz. It is shown that the anti-self-dual gauge fields on self-dual noncommutative R^4…
The study of Skyrmions predicts that there is an icosahedrally symmetric charge seventeen SU(2) Yang-Mills instanton in which the topological charge density, for fixed Euclidean time, is localized on the edges of the truncated icosahedron…
We present the detailed derivation of the charge one periodic instantons - or calorons - with non-trivial holonomy for SU(2). We use a suitable combination of the Nahm transformation and ADHM techniques. Our results rely on our ability to…
We examine the effect of a non-trivial nut charge on the action of non-compact four-dimensional instantons with a U(1) isometry. If the instanton action is calculated by dimensionally reducing along the isometry, then the nut charge is…
We study the noncommutative version of the extended ADHM construction in the eight dimensional U(1) Yang-Mills theory. This construction gives rise to the solutions of the BPS equations in the Yang-Mills theory, and these solutions preserve…