Related papers: Deconstructing Monopoles and Instantons
We present a simple alternative to Mackey's account of the (infinite) inequivalent quantizations possible on a coset space G/H. Our reformulation is based on the reduction ${\rm G \rightarrow G/H}$ and employs a generalized form of Dirac's…
We establish an isomorphism between the stable homotopy groups of the 2-completed motivic sphere spectrum over the real numbers and the corresponding stable homotopy groups of the 2-completed Z/2-equivariant sphere spectrum, in a certain…
In this article we compute the mapping class group of the total space $S(\xi)$ of the sphere bundle of a 3-dimensional real vector bundle $\xi$ over the complex projective plane $\mathbb{P}^2$ with $\langle p_1(\xi), [\mathbb{P}^2] \rangle…
In previous work, the second author defined 'equivariant instanton homology groups' $I^\bullet(Y,\pi;R)$ for a rational homology 3-sphere $Y$, a set of auxiliary data $\pi$, and a PID $R$. These objects are modules over the cohomology ring…
We propose a notion of instanton bundle (called $H$-instanton bundle) on any projective variety of dimension three polarized by a very ample divisor $H$, that naturally generalizes the ones on $\mathbb{P}^3$ and on the flag threefold…
We study some generalized instanton algebras which are required to describe `instantonic complex rank 2 bundles'. The spaces on which the bundles are defined are not prescribed from the beginning but rather are obtained from some natural…
We classify equivariant topological complex vector bundles over real projective plane under a compact Lie group (not necessarily effective) action. It is shown that nonequivariant Chern classes and isotropy representations at (at most)…
The classification of the $2$-designs with $\lambda=2$ admitting a flag-transitive automorphism groups with socle $PSL(2,q)$ is completed by settling the two open cases in \cite{ABDT}. The result is achieved by using conics and hyperovals…
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…
We point out that there exists a generalization of instanton symmmetry in the Coulomb phase of 5d nonabelian gauge theories which is capable of measuring a wider class of topological charges of monopole strings. The symmetry is invertible…
Using a homological invariant together with an obstruction class in a certain Ext^2-group, we may classify objects in triangulated categories that have projective resolutions of length two. This invariant gives strong classification results…
We consider Dirac monopoles embedded into SU(N) gauge theory with theta-term for $\theta = 4\pi M $ (where $M$ is half-integer for $N = 2$ and is integer for $N>2$). Due to the theta - term those monopoles obtain the SU(N) charge and become…
We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…
Two dimensional massless Dirac Hamiltonian under the influence of hyperbolic magnetic fields is mentioned in curved space. Using a spherical surface parametrization, the Dirac operator on the sphere is presented and the system is given as…
We apply the methods recently developed for computation of type IIA disk instantons using mirror symmetry to a large class of D-branes wrapped over Lagrangian cycles of non-compact Calabi-Yau 3-folds. Along the way we clarify the notion of…
We give some remarks on twisted determinant line bundles and Chern-Simons topological invariants associated with real hyperbolic manifolds. Index of a twisted Dirac operator is derived. We discuss briefly application of obtained results in…
In Refs.[1-4] Dirac and Schwinger showed the existence of a magnetic monopole required a charge quantization condition which we write following Dirac as $\frac{eg}{4\pi\hbar}=\frac{n}{2},\; n=0,\pm 1,\; \pm 2, \ldots$. Here, $g$ is the…
We introduce a spherical variant of Milnor's classifying construction for diffeological groups, based on quadratic normalization of barycentric coordinates. This construction gives rise to a contractible diffeological space endowed with…
We consider a gauge-Higgs system on a fuzzy 2-sphere and study the topological structure of gauge configurations, when the U(2) gauge symmetry is spontaneously broken to U(1) times U(1) by the vev of the Higgs field. The topology is…
Monopole-like objects have been identified in multiple lattice studies, and there is now a significant amount of literature on their importance in phenomenology. Some analytic indications of their role, however, are still missing. The 't…