Related papers: Octonionic Yang-Mills Instanton on Quaternionic Li…

In the pure Einstein-Yang-Mills theory in four dimensions there exist monopole and dyon solutions. The spectrum of the solutions is discrete in asymptotically flat or de Sitter space, whereas it is continuous in asymptotically anti-de…

We present a construction of self-dual Yang-Mills connections on the Taub-NUT space. We illustrate it by finding explicit expressions for all SU(2) instantons of instanton number one and generic monodromy at infinity.

We consider vortex-type solutions in $d=5$ dimensions of the Einstein gravity coupled to a nonabelian SU(2) field posessing a nonzero electric part. After the dimensional reduction, this corresponds to a $d=4$…

We revisit the problem of constructing instantons on ADE orbifolds R^4/\Gamma and point out some subtle relations with the complex structure on the orbifold. We consider generalized instanton equations on R^4/\Gamma which are BPS equations…

Using gauge theory for Spin(7)-manifolds of dimension 8, we develop a procedure, called Spin-rotation, which transforms a (stable) holomorphic structure on a vector bundle over a complex torus of dimension 4 into a new holomorphic structure…

We present arguments for the existence of self-dual Yang-Mills instantons for several spherically symmetric backgrounds with Euclidean signature. The time-independent Yang-Mills field has finite action and a vanishing energy momentum tensor…

We use the recursive structure of the compactification of the instanton moduli space of N=2 Super Yang-Mills theory with gauge group SU(2), to construct, by inductive limit, a universal moduli space which includes all the multi-instanton…

In this paper we prove that over an asymptotically locally flat (ALF) Riemannian four-manifold the energy of an "admissible" SU(2) Yang--Mills is always integer. This result sharpens the previously known energy identity for such Yang--Mills…

A concrete model for a 7-dimensional gauge theory under special holonomy is proposed, within the paradigm outlined by Donaldson and Thomas, over the asymptotically cylindrical G2-manifolds provided by Kovalev's noncompact version of the…

Interpreting the coordinates of the quantum Euclidean space R_q^4 [the SO_q(4)-covariant noncommutative space] as the entries of a ``q-quaternion matrix'' we construct (anti)instanton solutions of a would-be q-deformed su(2) Yang-Mills…

We construct a consistent set of monopole equations on eight-manifolds with Spin(7) holonomy. These equations are elliptic and admit non-trivial solutions including all the 4-dimensional Seiberg-Witten solutions as a special case.

We explore the correspondence between Yang-Mills instantons and algebraic curves. The curve is defined by Higgs zero locus of dyonic instantons in 1+4 dimensional Yang-Mills-Higgs theory, and it is identified in string theory with the…

We show how to find explicit expressions for rigid string instantons for general 4-manifold $M$. It appears that they are pseudo-holomorphic curves in the twistor space of $M$. We present explicit formulae for $M=R^4, S^4$. We discuss their…

We construct new explicit non-singular metrics that are complete on non-compact Riemannian 8-manifolds with holonomy Spin(7). One such metric, which we denote by A_8, is complete and non-singular on R^8. The other complete metrics are…

It is well known that there are no static non-Abelian monopole solutions in pure Yang-Mills theory on Minkowski space R^{3,1}. We show that such solutions exist in SU(N) gauge theory on the spaces R^2\times S^2 and R^1\times S^1\times S^2…

We develop the deformation theory of instantons on asymptotically conical $Spin(7)$-manifolds where the instanton is asymptotic to a fixed nearly $G_2$-instanton at infinity. By relating the deformation complex with spinors, we identify the…

Metrics of exceptional holonomy are vacuum solutions to the Einstein equation. In this paper we describe manifolds with holonomy contained in Spin(7) preserved by a three-torus symmetry in terms of tri-symplectic geometry of four-manifolds.…

In this paper we show how hypercomplex function theoretical objects can be used to construct explicitly self-dual SU(2)-Yang-Mills instanton solutions on certain classes of conformally flat 4-manifolds. We use a hypercomplex argument…

We develop a new construction of complete non-compact 8-manifolds with Riemannian holonomy equal to $\operatorname{Spin}(7)$. As a consequence of the holonomy reduction, these manifolds are Ricci-flat. These metrics are built on the total…

We study finite action anti-self-dual Yang-Mills connections on the multi-Taub-NUT space. We establish the curvature and the harmonic spinors decay rates and compute the index of the associated Dirac operator. This is the first in a series…