Related papers: Convergence of Yang-Mills-Higgs fields
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…
We study Nahm transformation for parabolic Higgs bundles on the projective line \PP^1, with logarithmic singularities on a finite set P. Such a Higgs bundle can be given by its spectral data: a Hirzebruch surface Z together with a coherent…
We compute solutions to the Hermitian Yang-Mills equations on holomorphic vector bundles $V$ via an alternating optimisation procedure founded on geometric machine learning. The proposed method is fully general with respect to the rank and…
A surface of codimension higher than one embedded in an ambient space possesses a connection associated with the rotational freedom of its normal vector fields. We examine the Yang-Mills functional associated with this connection. The…
In this note we introduce a Yang-Mills bar equation on complex vector bundles over compact Hermitian manifolds as the Euler-Lagrange equation for a Yang-Mills bar functional. We show the existence of a non-trivial solution of this equation…
This thesis is dedicated to the study of certain loci of the Higgs bundle moduli space on a compact Riemann surface. Motivated by mirror symmetry, we give a detailed description of the fibres of the $G$-Hitchin fibration containing…
The main goal of this paper is to generalize a part of the relationship between mean curvature and Harder-Narasimhan filtrations of holomorphic vector bundles to arbitrary polarized fibrations. More precisely, for a polarized family of…
We study SU(2) three-dimensional Yang-Mills theories in presence of Higgs fields in the light of the Gribov phenomenon. By restricting the domain of integration in the functional integral to the first Gribov horizon, we are able to discuss…
By considering a (partial) topological twisting of supersymmetric Yang-Mills compactified on a 2d space with `t Hooft magnetic flux turned on we obtain a supersymmetric $\sigma$-model in 2 dimensions. For N=2 SYM this maps Donaldson…
Co-Higgs bundles are Higgs bundles in the sense of Simpson, but with Higgs fields that take values in the tangent bundle instead of the cotangent bundle. Given a vector bundle on P^1, we find necessary and sufficient conditions on its…
Within the mathematical framework of Quillen, one interprets the Higgs field as part of the superconnection on a superbundle. We propose to take as superbundle the exterior algebra obtained from a Hermitian bundle with structure group U(n).…
A classification of gravitating Yang--Mills systems in all dimensions is presented. These systems are set up so that they support finite energy solutions. Both regular and black hole solutions are considered, the former being the limit of…
Based on Teichm\"uller theory, we construct a degenerating family $\overline{Y}_g^{orb} \rightarrow \overline{M}_g^{orb}$ over the Deligne-Mumford compactification of the moduli space with the natural orbifold structure such that any…
We consider the moduli space of semistable Higgs bundles on a smooth projective curve. Motivated by mirror symmetry, Hausel and Hitchin showed that over an open of the locus of smooth Hitchin fibers, the duality of Donagi-Pantev intertwines…
We quantize pure 2d Yang-Mills theory on an arbitrary Riemann surface in the gauge where the field strength is diagonal. Twisted sectors originate, as in Matrix string theory, from permutations of the eigenvalues around homotopically…
We discuss the twistor correspondence between complex vector bundles over a self-dual four-dimensional manifold and holomorphic bundles over its twistor space and describe the moduli space of self-dual Yang-Mills fields in terms of Cech and…
We propose a massive Yang-Mills model blessed with both physical unitarity and renormalizability without Higgs particles. This is achieved by a novel nonlinear but local transformation from the original fields in the Curci-Ferrari model to…
In this paper, we shall prove that, on a non-flat Riemannian vector bundle over a compact Riemannian manifold, the smooth solution of the Yang-Mills flow will blow up in finite time if the energy of the initial connection is small enough.…
We study topologically trivial $G$-Higgs bundles over an elliptic curve $X$ when the structure group $G$ is a connected real form of a complex semisimple Lie group $G^{\mathbb{C}}$. We achieve a description of their (reduced) moduli space,…
We give a differential geometric construction of the holomorphic family of Higgs bundle moduli spaces over a curve C as a fibration over Teichm\"uller space. The method uses a function f defined on the character variety, essentially the…