Related papers: The Haydys monopole equation
We study moduli spaces of solutions to the extended Bogomolny equations on $\Sigma \times \mathbb{R_{+,y}}$ with gauge group $\operatorname{SL}(2,\mathbb{C})$ satisfying the generalized Nahm pole boundary condition as $y\to 0$ and limiting…
We study intersecting brane systems that realize a class of singular monopole configurations in four-dimensional Yang-Mills-Higgs theory. Singular monopoles are solutions to the Bogomolny equation on R^3 with a prescribed number of…
We study Bogomolny equations on $R^2\times S^1$. Although they do not admit nontrivial finite-energy solutions, we show that there are interesting infinite-energy solutions with Higgs field growing logarithmically at infinity. We call these…
We study the Yang-Mills-Higgs system within the framework of general relativity. In the static situation, using Bogomol'nyi type analysis, we derive a positive-definite energy functional which has a lower bound. Specializing to the gauge…
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…
This thesis contains work which appeared in several papers. Additionally to the results in the papers it contains a detailed introduction and some further proofs and remarks. The dissertation gives a description of the topology and…
In this paper, we study the analytic properties of solutions to the Vafa-Witten equation over a compact Kaehler manifold. Simple obstructions to the existence of nontrivial solutions are identified. The gauge theoretical compactness for the…
Our aim in this work is to study a system of equations which generalises at the same time the vortex equations of Yang-Mills-Higgs theory and the holomorphicity equation in Gromov theory of pseudoholomorphic curves. We extend some results…
In this paper we consider a canonical compactification of Hitchin's moduli space of stable Higgs bundles with fixed determinant of odd degree over a Riemann surface, producing a projective variety by gluing in a divisor at infinity. We give…
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…
Moduli space of the Bogomolny equation on R^3 with certain asymptotic conditions at infinity has been well studied for a long time. This paper studies the moduli space of solutions to the Bogomolny equation on R^3 with a knot singularity.…
We develop a Kobayashi-Hitchin correspondence for the extended Bogomolny equations, i.e., the dimensionally reduced Kapustin-Witten equations, on the product of a compact Riemann surface $\Sigma$ with ${\mathbb R}^+_y$, with generalized…
Arising from a topological twist of $\mathcal{N} = 4$ super Yang-Mills theory are the Kapustin-Witten equations, a family of gauge-theoretic equations on a four-manifold parametrized by $t\in\mathbb{P}^1$. The parameter corresponds to a…
We use the multimonopole moduli space as a tool for studying the properties of BPS monopoles carrying nonabelian magnetic charges. For configurations whose total magnetic charge is purely abelian, the moduli space for nonabelian breaking…
We discuss the structure of the framed moduli space of Bogomolny monopoles for arbitrary symmetry breaking and extend the definition of its stratification to the case of arbitrary compact Lie groups. We show that each stratum is a union of…
We find both analytical and numerical solutions of SU(2) Yang-Mills with an adjoint Higgs field within both closed and open tubes whose sections are spherical caps. This geometry admits a smooth limit in which the space-like metric is flat…
In arXiv:0805.2192, we set up a gauge-theoretic equation on symplectic 6-manifolds, which is a version of the Hermitian-Einstein equation perturbed by Higgs fields, and call Donaldson-Thomas equation, to analytically approach the…
We obtain all possible solutions of a 1/4 Bogomol'nyi-Prasad-Sommerfield equation exactly, containing configurations made of walls, vortices and monopoles in the Higgs phase. We use supersymmetric U(N_C) gauge theories with eight…
We extend Hitchin's results on "The self-duality equations on a Riemann surface" (Proc. LMS (3), vol. 55, 1987) to orbifold Riemann surfaces. We prove existence results for orbifold solutions of the Yang-Mills-Higgs equations and construct…
There is an isomorphism between the moduli spaces of $\sigma$-stable holomorphic triples and some of the critical submanifolds of the moduli space of $k$-Higgs bundles of rank three, whose elements $(E,\varphi^k)$ correspond to variations…