Related papers: Comments on the U(2) Noncommutative Instanton
We review some recent progress in understanding the relation between a six dimensional topological Yang-Mills theory and the enumerative geometry of Calabi-Yau threefolds. The gauge theory localizes on generalized instanton solutions and is…
We construct explicit solutions of the Hermitian Yang-Mills equations on the noncommutative space C^n_\theta. In the commutative limit they coincide with the standard instantons on CP^n written in local coordinates.
An exact multimonopole solution of heterotic string theory is presented. The solution is constructed by a modification of the 't Hooft ansatz for a four-dimensional instanton. An analogous solution in Yang-Mills field theory saturates a…
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 construct the n-instanton action for the above model with gauge group SU(2), as a function of the collective coordinates of the general self-dual configurations of Atiyah, Drinfeld, Hitchin and Manin (ADHM). We calculate the quantum…
We present and discuss explicit solutions to the non-abelian self-dual string equation as well as to the non-abelian self-duality equation in six dimensions. These solutions are generalizations of the 't Hooft-Polyakov monopole and the BPST…
We show that every gravitational instantons are SU(2) Yang-Mills instantons on a Ricci-flat four manifold although the reverse is not necessarily true. It is shown that gravitational instantons satisfy exactly the same self-duality equation…
It is argued that whereas supersymmetry requires the instanton contribution to the expectation value of a straight Wilson line in the N=4 supersymmetric SU(2) Yang-Mills theory to vanish, it is not required to vanish in the case of a…
We search for an abelian description of the Yang-Mills instantons on certain eight dimensional manifolds with the special holonomies $Spin(7)$ and SU(4). By mimicing the Seiberg-Witten theory in four dimensions, we propose a set of…
A new classical solution for the SU(2) Yang-Mills theory, in which the Euclidean energy plays a role of a parameter is found. A correspondence between this solution and the known selfdual multi-instanton configuration, which has the…
We show that the apparently periodic Charap-Duff Yang-Mills `instantons' in time-compactified Euclidean Schwarzschild space are actually time independent. For these solutions, the Yang-Mills potential is constant along the time direction…
Several results on existence and convergence of the Yang-Mills flow in dimension four are given. We show that a singularity modeled on an instanton cannot form within finite time. Given low initial self-dual energy, we then study…
In this paper, we present all constant solutions of the Yang-Mills equations with ${\rm SU}(2)$ gauge symmetry for an arbitrary constant non-Abelian current in Euclidean space ${\mathbb R}^n$ of arbitrary finite dimension $n$. Using the…
We discuss the N=2 SU(2) Yang-Mills theory coupled with a massive matter in the weak coupling. In particular, we obtain the instanton expansion of its prepotential. Instanton contributions in the mass-less limit are completely reproduced.…
The SL(2,C) Yang-Mills instanton solutions constructed recently by the biquaternion method were shown to satisfy the complex version of the ADHM equations and the Monad construction. Moreover, we discover that, in addition to the…
We study bubbling phenomena of anti-self-dual instantons on $\H^2\times\S$, where $\S$ is a closed Riemann surface. The restriction of the instanton to each boundary slice $\{z\}\times\S$, $z\in\pd\H^2$ is required to lie in a Lagrangian…
We consider the self-dual Yang-Mills equations in seven dimensions. Modifying the t'Hooft construction of instantons in $d=4$, we find $N$-instanton $7d$ solutions which depend on $8N$ effective parameters and are $E_{6}$-invariant.
We present Backlund transformations for the noncommutative anti-self-dual Yang-Mills equation where the gauge group is G=GL(2) and use it to generate a series of exact solutions from a simple seed solution. The solutions generated by this…
We successfully exhaust the complete set of exact solutions of non-Abelian vortices in a quiver gauge theory, that is, the S[U(N) x U(N)] gauge theory with a bi-fudamental scalar field on a hyperbolic plane with a certain curvature, from…
We give a complete description of the behaviour of Calabi-Yau instantons and monopoles with an $SU(2)^2$-symmetry, on Calabi-Yau 3-folds with asymptotically conical geometry and $SU(2)^2$ acting with co-homogeneity one. We consider gauge…