Related papers: Instantons and Bows for the Classical Groups
Instantons on the Taub-NUT space are related to `bow solutions' via a generalization of the ADHM-Nahm transform. Both are related to complex geometry, either via the twistor transform or via the Kobayashi-Hitchin correspondence. We explore…
Yang-Mills instantons on ALE gravitational instantons were constructed by Kronheimer and Nakajima in terms of matrices satisfying algebraic equations. These were conveniently organized into a quiver. We construct generic Yang-Mills…
The moduli space of instantons on an ALE space is studied using the moduli space of $\mathcal{N}=4$ field theories in three dimensions. For instantons in a simple gauge group $G$ on $\mathbb{C}^2/\mathbb{Z}_n$, the Hilbert series of such an…
We study the moduli spaces of self-dual instantons on CP^2 in a simple group G. When G is a classical group, these instanton solutions can be realised using ADHM-like constructions which can be naturally embedded into certain three…
We present ADHM-Nahm data for instantons on the Taub-NUT space and encode these data in terms of Bow Diagrams. We study the moduli spaces of the instantons and present these spaces as finite hyperkahler quotients. As an example, we find an…
We investigate quantum effects on the Coulomb branch of three-dimensional N=4 supersymmetric gauge theory with gauge group SU(2). We calculate perturbative and one-instanton contributions to the Wilsonian effective action using standard…
On an oriented, compact, connected, real four-dimensional manifold, $M$, we introduce a topological Lagrangian gauge field theory with a Bogomol'nyi structure that leads to non-singular, finite-Action, stable solutions to the variational…
We describe the modern formalism, ideas and applications of the instanton calculus for gauge theories with, and without, supersymmetry. Particular emphasis is put on developing a formalism that can deal with any number of instantons. This…
Unitary anti-self-dual connections on Asymptotically Locally Flat (ALF) hyperk\"ahler spaces are constructed in terms of data organized in a bow. Bows generalize quivers, and the relevant bow gives rise to the underlying ALF space as the…
ALE and Taub-NUT (or ALF) hyper-Kahler four-manifolds can be naturally constructed as hyper-Kahler quotients. In the ALE case, this construction has long been understood in terms of D-branes; here we give a D-brane derivation in the…
We describe the explicit construction of Yang-Mills instantons on ALE spaces, following the work of Kronheimer and Nakajima. For multicenter ALE metrics, we determine the abelian instanton connections which are needed for the construction…
The index bundle of a family of Dirac operators associated to an instanton on a multi-Taub-NUT space forms a bow representation. We prove that the gauge equivalence classes of solutions of this bow representation are in one-to-one…
We discuss the Atiyah-Drinfeld-Hitchin-Manin (ADHM) construction of U(N) instantons in noncommutative (NC) space and prove the one-to-one correspondence between moduli spaces of the noncommutative instantons and the ADHM data, together with…
The moduli space of k G-instantons on R^4 for a classical gauge group G is known to be given by the Higgs branch of a supersymmetric gauge theory that lives on Dp branes probing D(p + 4) branes in Type II theories. For p = 3, these (3 + 1)…
Recently N.Nekrasov and A.Schwarz proposed a modification of the ADHM construction of instantons which produces instantons on a noncommutative deformation of the 4-dimensional real affine space. In this paper we study the relation between…
We generalize the recently proposed noncommutative ADHM construction to the case of $\Gamma$-equivariant instantons over $\R^4$, with $\Gamma$ a Kleinian group. We show that a certain form of the inhomogeneous ADHM equations describes…
We consider cones over manifolds admitting real Killing spinors and instanton equations on connections on vector bundles over these manifolds. Such cones are manifolds with special (reduced) holonomy. We generalize the scalar ansatz for a…
The moduli space of instantons on C^2 for any simple gauge group is studied using the Coulomb branch of N=4 gauge theories in three dimensions. For a given simple group G, the Hilbert series of such an instanton moduli space is computed…
Explicit construction of the basic SU(2) anti-instantons over the multi-Taub--NUT geometry via the classical conformal rescaling method is exhibited. These anti-instantons satisfiy the so-called weak holonomy condition at infinity with…
Gieseker-Nakajima moduli spaces $M_{k}(n)$ parametrize the charge $k$ noncommutative $U(n)$ instantons on ${\bf R}^{4}$ and framed rank $n$ torsion free sheaves $\mathcal{E}$ on ${\bf C\bf P}^{2}$ with ${\rm ch}_{2}({\mathcal{E}}) = k$.…