Related papers: Instantons on the six-sphere and twistors

We revisit the problem of constructing instantons on ADE orbifolds R^4/\Gamma and point out some subtle relations with the complex structure on the orbifold. We consider generalized instanton equations on R^4/\Gamma which are BPS equations…

We study homogeneous instantons on the seven dimensional Stiefel manifold V in the context of $G_2$ and Sasakian geometry. According to the reductive decomposition of V we provide an explicit description of all invariant $G_2$ and Sasakian…

We consider Lie G-valued Yang-Mills fields on the space R x G/H, where G/H is a compact nearly K"ahler six-dimensional homogeneous space, and the manifold R x G/H carries a G_2-structure. After imposing a general G-invariance condition,…

We study quiver gauge theories on the round and squashed seven-spheres, and orbifolds thereof. They arise by imposing $G$-equivariance on the homogeneous space $G/H=\mathrm{SU}(4)/\mathrm{SU}(3)$ endowed with its Sasaki-Einstein structure,…

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…

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 consider the partition function for Euclidean $SU(N)$ super Yang-Mills on a squashed seven-sphere. We show that the localization locus of the partition function has instanton membrane solutions wrapping the six "fixed" three-spheres on…

We study $\mathfrak{g}$-valued Yang-Mills fields on cylinders $Z(G/H)=\mathbb{R} \times G/H$, where G/H is a compact seven-dimensional coset space with $G_2$-structure, $\mathfrak{g}$ is the Lie algebra of G, and Z(G/H) inherits a…

This is a self-contained set of lecture notes on instantons in (super) Yang-Mills theory in four dimensions and in quantum mechanics. First the basics are derived from scratch: the regular and singular one-instanton solutions for Yang-Mills…

We explore the correspondence between Yang-Mills instantons and algebraic curves. The curve is defined by Higgs zero locus of dyonic instantons in 1+4 dimensional Yang-Mills-Higgs theory, and it is identified in string theory with the…

We consider a dimensional reduction of the (deformed) Hermitian Yang-Mills condition on $S^1$-invariant K\"ahler Einstein $6$-manifolds. This allows us to reformulate the (deformed) Hermitian Yang-Mills equations in terms of data on the…

Let M be a G2-manifold. We consider an almost CR-structure on the sphere bundle of unit tangent vectors on M, called the CR twistor space. This CR-structure is integrable if and only if M is a holonomy G2 manifold. We interpret G2-instanton…

We construct the half-supersymmetric instanton solutions that are electric-magnetically dual to the recently discussed half-supersymmetric Q7-branes. We call these instantons `Q-instantons'. Whereas the D-instanton is most conveniently…

The nearly K\"{a}hler structures on the 6-sphere, as a twistor bundle sections are researched. We show that for any point of twistor bundle there exists an 1-parametric family of sections, passing through the point, which give nearly…

In this note, we revisit some well-known examples of instantons on flat space that were originally discovered in the physics literature. In particular, we explain how the basic instanton on $\mathbb{R}^4$, with its flat hyperkaehler…

We present a construction of self-dual Yang-Mills connections on the Taub-NUT space. We illustrate it by finding explicit expressions for all SU(2) instantons of instanton number one and generic monodromy at infinity.

This is an expository article on the 1978 Atiyah-Drinfeld-Hitchin-Manin construction of Yang-Mills instanton connections over the 4-sphere.

The study of Skyrmions predicts that there is an icosahedrally symmetric charge seventeen SU(2) Yang-Mills instanton in which the topological charge density, for fixed Euclidean time, is localized on the edges of the truncated icosahedron…

We report results obtained for SU(2) Yang-Mills theory on a four dimensional torus with two directions much smaller than the other two. The small 2-torus is equipped with twisted boundary conditions. This construction provides a way to…

We study finite action anti-self-dual Yang-Mills connections on the multi-Taub-NUT space. We establish the curvature and the harmonic spinors decay rates and compute the index of the associated Dirac operator. This is the first in a series…