Related papers: Noncommutative Monopoles and Riemann-Hilbert Probl…
With the help of the Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2) Yang-Mills field, we find an integrable subsystem of SU(2) Yang-Mills theory coupled to the dilaton. Here integrability means the existence of infinitely many…
We study static spherically-symmetric solutions of non-Abelian gauge theory coupled to Conformal Gravity. We find solutions for the self-gravitating pure Yang-Mills case as well as monopole-like solutions of the Higgs system. The former are…
We observe that the main feature of the Randall-Sundrum model, used to solve the hierarchy problem, is already present in a class of Yang-Mills plus gravity theories inspired by noncommutative geometry. Strikingly the same expression for…
We consider self-dual Yang-Mills instantons in 4-dimensional Kaehler spaces with one holomorphic isometry and show that they satisfy a generalization of the Bogomol'nyi equation for magnetic monopoles on certain 3-dimensional metrics. We…
Let $(X, \omega)$ be a compact connected Hermitian manifold of dimension $n$. We consider the Bott-Chern cohomology and let $[\chi ] \in H^{1,1}_{\text{BC}}(X; \mathbb{R})$. We study the deformed Hermitian-Yang-Mills equation, which is the…
Two families of SO(2n) Higgs models in $2n$ dimensional spacetime are presented. One family arises from the {\it dimensional reduction} of higher dimensional Yang-Mills systems while the construction of the other one is {\it ad hoc}, the…
The existence of nonsingular classical magnetic monopole solutions is usually understood in terms of topologically nontrivial Higgs field configurations. We show that finite energy magnetic monopole solutions also exist within a class of…
We determine the asymptotic dynamics of the U(N) doubly periodic BPS monopole in Yang-Mills-Higgs theory, called a monopole wall, by exploring its Higgs curve using the Newton polytope and amoeba. In particular, we show that the monopole…
A tensor product generalisation of $B\wedge F$ theories is proposed to give a Bogomol'nyi structure. Non-singular, stable, finite-energy particle-like solutions to the Bogomol'nyi equations are studied. Unlike Yang-Mills(-Higgs) theory, the…
The abelian Higgs model on the noncommutative plane admits both BPS vortices and non-BPS fluxons. After reviewing the properties of these solitons, we discuss several new aspects of the former. We solve the Bogomoln'yi equations…
The endpoint of this series of papers is to construct the monopole Floer homology for any pair $(Y,\omega)$, where $Y$ is a compact oriented 3-manifold with toroidal boundary and $\omega$ is a suitable closed 2-form. In the first paper, we…
We summarize recent results on the resolution of two intimately related problems, one physical, the other mathematical. The first deals with the resolution of the non-perturbative low energy dynamics of certain N=2 supersymmetric Yang-Mills…
We present a powerful method to generate various equations which possess the Lax representations on noncommutative (1+1) and (1+2)-dimensional spaces. The generated equations contain noncommutative integrable equations obtained by using the…
We consider a most general $SU(2)$ Yang-Mills-Higgs model consist of terms up to quadratic in first-derivative of the fields, that is the generalized $SU(2)$ Yang-Mills-Higgs with additional scalars-dependent coupling $\theta$-term. Using…
In the present paper it is shown that the Yang-Mills equation can be represented as the equation of the non-linear electromagnetic waves superposition. The research of the topological characteristics of this representation allows us to…
We consider matrix orthogonal polynomials related to Jacobi type matrices of weights that can be defined in terms of a given matrix Pearson equation. Stating a Riemann-Hilbert problem we can derive first and second order differential…
The Dirac-Yang monopoles are singular Yang--Mills field configurations in all Euclidean dimensions. The regular counterpart of the Dirac monopole in D=3 is the t Hooft-Polyakov monopole, the former being simply a gauge transform of the…
We prove the existence of the gravitating BPS monopole in Einstein-Yang-Mills-Higgs (EYMH) theory. Existence is established using a Newtonian perturbation argument which shows that a Yang-Mills-Higgs BPS monopole solution can be be…
We construct the first nontrivial examples of Calabi-Yau monopoles. Our main interest on these, comes from Donaldson and Segal's suggestion \cite{Donaldson2009} that it may be possible to define an invariant of certain noncompact Calabi-Yau…
We consider singly periodic solutions to the SU(2) Bogomolny equations and use the Nahm transform to generate a class of monopoles of charge k>2, thereby extending known results for lower charge chains. Some simple scattering processes are…