Related papers: Remarks on the complex geometry of the 3-monopole
We develop the Ercolani-Sinha construction of SU(2) monopoles and make this effective for (a five parameter family of centred) charge 3 monopoles. In particular we show how to solve the transcendental constraints arising on the spectral…
Monopoles are solutions of an SU(2) gauge theory in $\mathbb{R}^{3}$ satisfying a lower bound for energy and certain asymptotic conditions, which translate as topological properties encoded in their charge. Using methods from integrable…
We discuss the explicit formulation of the transcendental constraints defining spectral curves of SU(2) BPS monopoles in the twistor approach of Hitchin, following Ercolani and Sinha. We obtain an improved version of the Ercolani-Sinha…
We classify all possible charge-3 monopole spectral curves with non-trivial automorphism group and within these identify those with elliptic quotients. By focussing on elliptic quotients the transcendental constraints for a monopole…
We develop the Atiyah-Drinfeld-Manin-Hitchin-Nahm construction to study SU(2) non-abelian charge 3 monopoles within the algebro-geometric method. The method starts with finding an algebraic curve, the monopole spectral curve, subject to…
We determine the spectral curve of charge 3 BPS su(2) monopoles with C_3 cyclic symmetry. The symmetry means that the genus 4 spectral curve covers a (Toda) spectral curve of genus 2. A well adapted homology basis is presented enabling the…
We formulate a correspondence between SU(2) monopole chains and ``spectral data'', consisting of curves in $\mathbb{CP}^1\times\mathbb{CP}^1$ equipped with parabolic line bundles. This is the analogue for monopole chains of Donaldson's…
This article deals with a nonrelativistic quantum mechanical study of a charge-dyon system with the SU(2)--monopole in five dimensions. The Schr\"odinger equation for this system is separable in the hyperspherical and parabolic coordinates.…
We extend the investigation of BPS saturated t'Hooft-Polyakov monopoles in $\mathcal{M}^{2}\times S^{2}$ to the general case of $SU(N)$ gauge symmetry. This geometry causes the resulting $N-1$ coupled non-linear ordinary differential…
We study SU(2) BPS monopoles with spectral curves of the form $\eta^3+\chi(\zeta^6+b \zeta^3-1)=0$. Previous work has has established a countable family of solutions to Hitchin's constraint that $L^2$ was trivial on such a curve. Here we…
We discuss $SU(2)$ Bogomolny monopoles of arbitrary charge $k$ invariant under various symmetry groups. The analysis is largely in terms of the spectral curves, the rational maps, and the Nahm equations associated with monopoles. We…
According to the proposal of Hanany and Witten, Coulomb branches of N=4 SU(n) gauge theories in three dimensions are isometric to moduli spaces of BPS monopoles. We generalize this proposal to gauge theories with matter, which allows us to…
We use the fermion zero-modes in the background of multi-caloron solutions with non-trivial holonomy as a probe for constituent monopoles. We find in general indication for an extended structure. However, for well separated constituents…
We define and study natural $\mathrm{SU}(2)$-structures, in the sense of Conti-Salamon, on the total space $\cal S$ of the tangent sphere bundle of any given oriented Riemannian 3-manifold $M$. We recur to a fundamental exterior…
In this report, in the framework of an analytical approach and with help of the generalized version of the Hurwitz transformation the five-dimensional SU(2)--monopole model is constructed from the eight-dimensional quantum oscillator. The…
Recently we have shown how one may use use integrable systems techniques to implement the ADHMN construction and obtain general analytic formulae for the charge n su(2) Euclidean monopole. Here we do this for the case of charge 2: so…
We discuss the ADHMN construction for SU(N) monopoles and show that a particular simplification arises in studying charge N-1 monopoles with minimal symmetry breaking. Using this we construct families of tetrahedrally symmetric SU(4) and…
We present explicit expressions for the fields of a charge one BPS monopole with two Dirac singularities. These are solutions of the nonlinear Bogomolny equations with the gauge group U(2) or SO(3). We derive these expressions by applying…
We construct M-theory curves associated with brane configurations of SU(N), SO(N) and $Sp(2N)$ 5d supersymmetric gauge theories compactified on a circle. From the curves we can account for all the existing different SU(N) field theories…
We construct multimonopole solutions containing N-1 distinct fundamental monopoles in SU(N) gauge theory. When the gauge symmetry is spontaneously broken to U(1)^{N-1}, the monopoles are all massive, and we show that the fields can be…