Related papers: Gauge theory and the division algebras

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 consider the Yang-Mills flow equations on a reductive coset space G/H and the Yang-Mills equations on the manifold R x G/H. On nonsymmetric coset spaces G/H one can introduce geometric fluxes identified with the torsion of the spin…

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…

We classify finite energy harmonic 2-forms on the asymptotically flat gravitational instanton constructed by Chen and Teo. We prove that every $U(1)$-bundle admits a unique anti-self-dual Yang-Mills instanton (up to gauge equivalence) which…

The arcane ADHM construction of Yang-Mills instantons can be very naturally understood in the framework of D-brane dynamics in string theory. In this point-of-view, the mysterious auxiliary symmetry of the ADHM construction arises as a…

We derive modular anomaly equations from the Seiberg-Witten-Donagi curves for softly broken N=4 SU(n) gauge theories. From these equations we can derive recursion relations for the pre-potential in powers of m^2, where m is the mass of the…

We systematically construct and study smooth supersymmetric solutions in 5 dimensional N=1 Yang-Mills-Einstein supergravity. Our solution is based on the ADHM construction of (dyonic) multi-instantons in Yang-Mills theory, which extends to…

We consider Euclidean SU(N) Yang-Mills theory on the space GxR, where G is a compact semisimple Lie group, and introduce first-order BPS-type equations which imply the full Yang-Mills equations. For gauge fields invariant under the adjoint…

A classification result for Ricci-flat anti-self-dual asymptotically locally Euclidean 4-manifolds is obtained: they are either hyperk\"ahler (one of the gravitational instantons classified by Kronheimer), or they are a cyclic quotient of a…

The classification of homogeneous quaternionic manifolds has been done by Alekseevskii, Wolf et al using transitive solvable group of isometries. These manifolds are not generically symmetric, but there is a subset of quaternionic manifolds…

We investigate instantons on manifolds with Killing spinors and their cones. Examples of manifolds with Killing spinors include nearly Kaehler 6-manifolds, nearly parallel G_2-manifolds in dimension 7, Sasaki-Einstein manifolds, and…

We study analytic aspects of U(n) gauge theory over a toric noncommutative manifold $M_\theta$. We analyse moduli spaces of solutions to the self-dual Yang-Mills equations on U(2) vector bundles over four-manifolds $M_\theta$, showing that…

We consider G-equivariant dimensional reduction of Yang-Mills theory with torsion on manifolds of the form MxG/H where M is a smooth manifold, and G/H is a compact six-dimensional homogeneous space provided with a never integrable almost…

We present a novel approach to the study of Yang-Mills instantons on quaternionic K\"ahler manifolds, based on an extension of the harmonic space method of constructing instantons on hyperk\"ahler manifolds. Our results establish a…

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 well-known Yang-Mills theory with one $ S^{1} / Z_{2}$ universal extra dimension (UED) is generalized to an arbitrary number of spatial extra dimensions through a novel compactification scheme. In this paper, the Riemannian flat based…

The partition function of four dimensional Euclidean, non-supersymmetric SU(2) Yang--Mills theory is calculated in the perturbative and weak coupling regime i.e. in a small open ball about the flat connection (what we call the vicinity of…

We survey some features of equivariant instanton partition functions of topological gauge theories on four and six dimensional toric Kahler varieties, and their geometric and algebraic counterparts in the enumerative problem of counting…

We discuss instantons on noncommutative four-dimensional Euclidean space. In commutative case one can consider instantons directly on Euclidean space, then we should restrict ourselves to the gauge fields that are gauge equivalent to the…

Subjecting the SU(2) Yang--Mills system to azimuthal symmetries in both the $x-y$ and the $z-t$ planes results in a residual subsystem described by a U(1) Higgs like model with two complex scalar fields on the quarter plane. The resulting…