Related papers: Dimension Reduction of Generalized ASD Instantons

We investigate Yang--Mills instanton theory over four dimensional asymptotically locally flat (ALF) geometries, including gravitational instantons of this type, by exploiting the existence of a natural smooth compactification of these…

Let $X$ be a closed $6-$dimensional manifold with a half-closed $SU(3)-$structure. On the product manifold $X\times S^{1}$, with respect to the product $G_{2}-$structure and on a pullback vector bundle from $X$, we show that any…

We discuss instantons in dimensions higher than four. A generalized self-dual or anti-self-dual instanton equation in n-dimensions can be defined in terms of a closed (n-4) form $\Omega$ and it was recently employed as a topological gauge…

Given a bundle gerbe with connection on an oriented Riemannian manifold of dimension at least equal to 3, we formulate and study the associated Yang-Mills equations. When the Riemannian manifold is compact and oriented, we prove the…

Studied are moduli spaces of self dual or anti-self dual connections on noncommutative 4-manifolds, especially deformation quantization of compact spin Riemannian 4-manifolds and their isometry groups have 2-torus subgroup. Then such moduli…

We extend equivariant dimensional reduction techniques to the case of quantum spaces which are the product of a Kaehler manifold M with the quantum two-sphere. We work out the reduction of bundles which are equivariant under the natural…

In this article we study the moduli space of conically singular instantons (or Hermitian Yang--Mills connections) with prescribed tangent connections over a 6-manifold equipped with an $\mathrm{SU}(3)$-structure. That is, we develop a…

Adjusting conventional Chern-Simons theory to ${\rm G}_2$-manifolds, one describes ${\rm G}_2$-instantons on bundles over a certain class of $7$-dimensional flat tori which fiber non-trivially over $T^4$, by a pullback argument. Moreover,…

We use the information metric to investigate the moduli space of a U(1) instanton on (anti)self-dual manifolds, finding an $AdS$ geometry similar to that for the moduli space of a Yang-Mills instanton on flat space. We discuss our results…

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…

We search for an abelian description of the Yang-Mills instantons on certain eight dimensional manifolds with the special holonomies $Spin(7)$ and SU(4). By mimicing the Seiberg-Witten theory in four dimensions, we propose a set of…

We consider the Hermitian Yang-Mills (instanton) equations for connections on vector bundles over a 2n-dimensional K\"ahler manifold X which is a product Y x Z of p- and q-dimensional Riemannian manifold Y and Z with p+q=2n. We show that in…

The anti-self-dual projection of the spin connections of certain four-dimensional Einstein manifolds can be Abelian in nature. These configurations signify bundle reductions. By a theorem of Kobayashi and Nomizu such a process is predicated…

Anti-self-dual (ASD) solutions to the Yang-Mills equation (or instantons) over an anti-self-dual four manifold, which are invariant under an appropriate action of a three dimensional Lie group, give rise, via twistor construction, to…

We prove an existence theorem for gauge invariant $L^2$-normal neighborhoods of the reduction loci in the space ${\cal A}_a(E)$ of oriented connections on a fixed Hermitian 2-bundle $E$. We use this to obtain results on the topology of the…

We consider $G_2$-structures with torsion coupled with $G_2$-instantons, on a compact $7$-dimensional manifold. The coupling is via an equation for $4$-forms which appears in supergravity and generalized geometry, known as the Bianchi…

The equivalence of the anti-selfduality Yang-Mills equations on the 4-dimensional orientable Riemannian manifold and Laplace equations for some infinite dimensional Laplacians is proved. A class of modificated Levy Laplacians parameterized…

We describe a glueing construction for a certain self-dual reduction of the Yang-Mills equations in dimension 8.

We study, by means of mirror symmetry, the quantum geometry of the K\"ahler-class parameters of a number of Calabi-Yau manifolds that have $b_{11}=2$. Our main interest lies in the structure of the moduli space and in the loci corresponding…

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…