Related papers: A monopole solution from noncommutative multi-inst…
Monopoles in topologically massive gauge theories in 2+1 dimensions with a Chern-Simon mass term have been studied by Pisarski some years ago. He investigated the SU(2) Yang-Mills-Higgs model with an additional Chern-Simon mass term in the…
We construct the first analytic examples of topologically non-trivial solutions of the (3+1)-dimensional $U(1)$ gauged Skyrme model within a finite box in (3+1)-dimensional flat space-time. There are two types of gauged solitons. The first…
Given a bundle gerbe with connection on an oriented Riemannian manifold of dimension at least equal to 3, we formulate and study the associated Yang-Mills equations. When the Riemannian manifold is compact and oriented, we prove the…
We use a numerical cooling algorithm to study fractional instantons in $SU(2)$ pure Yang-Mills on $\mathbb{R}^2\times\mathbb{T}^2_*$, $\mathbb{R}^3\times S^1$, and $\mathbb{R}\times \mathbb{T}^2_* \times S^1$. We confirm that the fractional…
In the previous paper, we have shown the existence of magnetic monopoles in the pure $SU(2)$ Yang--Mills theory with a gauge-invariant mass term for the gluon field being introduced. In this paper, we extend our previous construction of…
We discuss four-dimensional "spatially homogeneous" gravitational instantons. These are self-dual solutions of Euclidean vacuum Einstein's equations with potentially non-vanishing cosmological constant. They are endowed with a product…
A model of spherically symmetric SU(2) gauge theory is considered. The self-duality equations are written and it is shown that they are compatible with the Einstein-Yang-Mills equations. It is proven that this property is true for any gauge…
The self-duality equations for gauge fields in pseudoeuclidean spaces of eight and seven dimensions are considered. Some new classes of solutions of the equations are found.
We find non-trivial, time-dependent solutions of the (anti) self-dual Yang-Mills equations in the four dimensional Euclidean Anti-de Sitter space. In contrast to the Euclidean flat space, the action depends on the moduli parameters and the…
We find a class of exact solutions of noncommutative gauge theories corresponding to unstable non-BPS solitons. In the two-dimensional euclidean (or 2+1 dimensional lorentzian) U(1) theory we find localized solutions carrying nonzero…
We have recently introduced the notion of a q-quaternion bialgebra and shown its strict link with the SO_q(4)-covariant quantum Euclidean space R_q^4. Adopting the available differential geometric tools on the latter and the quaternion…
We study analytic aspects of U(n) gauge theory over a toric noncommutative manifold $M_\theta$. We analyse moduli spaces of solutions to the self-dual Yang-Mills equations on U(2) vector bundles over four-manifolds $M_\theta$, showing that…
This paper is concerned with magnetic monopole solutions of SU(3) Yang-Mills-Higgs system beyond the Bogomol'nyi-Prasad-Sommerfield limit. The different SU(2) embeddings, which correspond to the fundamental monopoles, as well the embedding…
We study the Einstein-Chern-Simons gravity coupled to Yang-Mills-Higgs theory in three dimensional Euclidean space with cosmological constant. The classical equations reduce to Bogomol'nyi type first order equations in curved space. There…
We construct the Picard-Fuchs equations of the $N=2$ supersymmetric $SU(2)$ gauge theories with $N_f=0,1,3$ matter multiplets. For the $N_f=0$ theory from the solutions of the Picard-Fuchs equation the monodromy matrices on the quantum…
By examining multi-instantons in N=2 supersymmetric SU(2) gauge theory, we derive, on very general grounds, and to all orders in the instanton number, a relationship between the prepotential F(Phi), and the coordinate on the quantum moduli…
We consider generalized self-duality equations for U(2r) Yang-Mills theory on R^{4k} with quaternionic structure and self-dual Moyal deformation. We employ the extended ADHM method in 4k dimensions to construct new noncommutative…
We discuss the modular anomaly equation satisfied by the the prepotential of 4-dimensional N=2* theories and show that its validity is related to S-duality. The recursion relations that follow from the modular anomaly equation allow one to…
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 consider an SU(4) Yang-Mills-Higgs theory spontaneously broken to $SO(4)$ by a scalar field in the $n\times n$ representation and the unbroken algebra invariant under Cartan automorphism. We obtain that $\mathbb Z_2$ monopoles in this…