相关论文: Convergence of Yang-Mills-Higgs fields

We review the notions of (weak) Hermitian-Yang-Mills structure and approximate Hermitian-Yang-Mills structure for Higgs bundles. Then, we construct the Donaldson functional for Higgs bundles over compact K\"ahler manifolds and we present…

We prove that a generically regular semisimple Higgs bundle equipped with a non-degenerate symmetric pairing on any Riemann surface always has a harmonic metric compatible with the pairing. We also study the classification of such…

We discuss geometrical aspects of Higgs systems and Toda field theory in the framework of the theory of vector bundles on Riemann surfaces of genus greater than one. We point out how Toda fields can be considered as equivalent to Higgs…

In this paper, we study Hermitian-Yang-Mills connections (HYM) on a smooth Hermitian vector bundle over compact K\"{a}hler manifold. We calculate the virtual dimension of the moduli space of HYM connections and provide an analytic proof…

Let $X$ be a compact connected K\"ahler--Einstein manifold with $c_1(TX)\, \geq\, 0$. If there is a semistable Higgs vector bundle $(E\,,\theta)$ on $X$ with $\theta\,\not=\,0$, then we show that $c_1(TX)=0$, any $X$ satisfying this…

We consider the gradient flow of the Yang-Mills-Higgs functional of twist Higgs pairs on a Hermitian vector bundle $(E,H_0)$ over a Riemann surface $X$. It is already known the gradient flow with initial data $(A_0,\phi_0)$ converges to a…

Given a flat gauge field $\nabla$ on a vector bundle $F$ over a manifold $M$ we deduce a necessary and sufficient condition for the field $\nabla+ E$, with $E$ an ${\rm End}(F)$-valued $1$-form, to be a Yang-Mills field. For each curve of…

We study the moduli space of Yang--Mills connections on bundles over a conformally compact manifold $\overline{M}$. We prove that, for every Yang--Mills connection $A$ that satisfies an appropriate nondegeneracy condition, and for every…

The main result of this paper is a construction of solutions to the reverse Yang-Mills-Higgs flow converging in the $C^\infty$ topology to a critical point. The construction uses only the complex gauge group action, which leads to an…

We generalize the Hitchin-Kobayashi correspondence between semistability and the existence of approximate Hermitian-Yang-Mills structures to the case of principal Higgs bundles. We prove that a principal Higgs bundle on a compact Kaehler…

Let A be the space of irreducible connections (vector potentials) over a SU(n)-principal bundle on a three-dimensional manifold M. Let T be the fiber product of the tangent and cotangent bundles of A. We endow T with a symplectic structure…

We study pure Yang--Mills theory on $\Sigma\times S^2$, where $\Sigma$ is a compact Riemann surface, and invariance is assumed under rotations of $S^2$. It is well known that the self-duality equations in this set-up reduce to vortex…

In "The Yang-Mills equations over Riemann surfaces", Atiyah and Bott studied Yang-Mills functional over a Riemann surface from the point of view of Morse theory. We generalize their study to all closed, compact, connected, possibly…

This paper concerns the relationship between locally homogeneous geometric structures on topological surfaces and the moduli of polystable Higgs bundles on Riemann surfaces, due to Hitchin and Simpson. In particular we discuss the…

Let M be a manifold with Grassmann structure, i.e. with an isomorphism of the cotangent bundle T^*M\cong E\otimes H with the tensor product of two vector bundles E and H. We define the notion of a half-flat connection \nabla^W in a vector…

Vortices and coupled vortices arise from Yang-Mills-Higgs theories and can be viewed as generalizations or analogues to Yang-Mills connections and, in particular, Hermitian-Yang-Mills connections. We proved an analytic compactification of…

We discuss cosmological models involving homogeneous and isotropic Yang-Mills (YM) fields. Such models were proposed recently as an alternative to scalar models of cosmic acceleration. There exists a unique SU(2) YM configuration…

This paper gives a construction, using heat kernels, of differential forms on the moduli space of metrised ribbon graphs, or equivalently on the moduli space of Riemann surfaces with boundary. The construction depends on a manifold with a…

This thesis contains work which appeared in several papers. Additionally to the results in the papers it contains a detailed introduction and some further proofs and remarks. The dissertation gives a description of the topology and…

We derive a generalization of the flat space Yang's and Newman's equations for self-dual Yang-Mills fields to (locally) conformally Kahler Riemannian 4-manifolds. The results also apply to Einstein metrics (whose full curvature is not…