Related papers: Uncoupled Dirac-Yang-Mills Pairs on Closed Riemann…

In this paper we construct examples of spherically symmetric Dirac-Yang-Mills pairs on Riemannian 3-manifolds with the structure group SU(2). This approach yields coupled solutions (i.e. the connection is not a Yang-Mills connection) and…

We show that for a suitable class of ``Dirac-like'' operators there holds a Gluing Theorem for connected sums. More precisely, if $M_1$ and $M_2$ are closed Riemannian manifolds of dimension $n\ge 3$ together with such operators, then the…

We present a result for non-compact manifolds with invertible Dirac operator, where we link the presence of a massless Killing spinor, with a harmonic, closed conformal Killing-Yano tensor, if one exists for the specic manifold. A couple of…

We consider Dirac operators on odd-dimensional compact spin manifolds which are twisted by a product bundle. We show that the space of connections on the twisting bundle which yield an invertible operator has infinitely many connected…

The existence of normalizable zero modes of the twisted Dirac operator is proven for a class of static Einstein-Yang-Mills background fields with a half-integer Chern-Simons number. The proof holds for any gauge group and applies to Dirac…

The article considers some concrete solutions to the Dirac equation coupled to a vector bundle with connection, arising in the study of Yang-Mills equations and vector bundles on Riemann surfaces.

We show that the self-dual Yang-Mills equations afford supersymmetrisation to systems of equations invariant under global N-extended super-Poincar\'e transformations for arbitrary values of N, without the limitation (N\le 4) applicable to…

In this paper (Part I) and its sequels (Part II and Part III), we analyze the structure of the space of solutions to the epsilon-Dirichlet problem for the Yang-Mills equations on the 4-dimensional disk, for small values of the coupling…

We consider a static, spherically symmetric system of a Dirac particle in a classical gravitational and SU(2) Yang-Mills field. We prove that the only black-hole solutions of the corresponding Einstein-Dirac-Yang/Mills equations are the…

A method for systematically including topological degrees of freedom in perturbation theory is developed. This is not bound by the restrictions of semi-classical techniques. The Yang-Mills theory in three Euclidean dimensions is considered…

We study a static, spherically symmetric system of (2j+1) massive Dirac particles, each having angular momentum j, j=1,2,..., in a classical gravitational and SU(2) Yang-Mills field. We show that for any black hole solution of the…

Self-dual gauge potentials admit supersymmetric couplings to higher-spin fields satisfying interacting forms of the first order Dirac--Fierz equation. The interactions are governed by conserved currents determined by supersymmetry. These…

The relation between two--dimensional integrable systems and four--dimen\-sional self--dual Yang--Mills equations is considered. Within the twistor description and the zero--curvature representation a method is given to associate self--dual…

We consider on a spin manifold with boundary a Dirac operator $D_A$ with chiral boundary conditions, twisted by a unitary connection $A$. When $m$ is not in the chiral spectrum of $D_A$, we define an analogue of the Dirichlet-to-Neumann map…

The harmonic sections of the Kaluza-Klein model can be seen as a variant of harmonic maps with additional gauge symmetry. Geometrically, they are realized as sections of a fiber bundle associated to a principal bundle with a connection. In…

We study 7D maximally supersymmetric Yang-Mills theory on curved manifolds that admit Killing spinors. If the manifold admits at least two Killing spinors (Sasaki-Einstein manifolds) we are able to rewrite the supersymmetric theory in terms…

Working over a pseudo-Riemannian manifold, for each vector bundle with connection we construct a sequence of three differential operators which is a complex (termed a Yang-Mills detour complex) if and only if the connection satisfies the…

Along the lines of the classic Hodge-De Rham theory a general decomposition theorem for sections of a Dirac bundle over a compact Riemannian manifold is proved by extending concepts as exterior derivative and coderivative as well as as…

We study four-dimensional $\mathrm{SU}(N)$ Yang-Mills theory on $\mathbb{R} \times \mathbb{T}^3=\mathbb{R} \times S^1_A \times S^1_B \times S^1_C$, with a twisted boundary condition by a $\mathbb{Z}_N$ center symmetry imposed on $S^1_B…

We study the clustering of the lowest non negative eigenvalue of the Dirac operator on a general Dirac bundle when the metric structure is varied. In the classical case we show that any closed spin manifold of dimension greater than or…