arXiv research

Removes singularities for Yang-Mills-Higgs fields in higher dimensions.

New energy functional and fields for Yang-Mills theory, proving monotonicity and vanishing theorems.

The paper studies decay near singularities of 3d Yang-Mills-Higgs fields.

Study proves uniqueness of Yang-Mills field tangent cones in arbitrary dimensions.

The paper studies gauge fields on coherent sheaves and their Yang-Mills properties.

Study on Yang-Mills fields on $S^4$ proving self-duality constraints.

The study refines stability results for Yang-Mills fields and harmonic maps.

Study Einstein-Yang-Mills fields on specific manifolds, proving field deformations.

Paper proves no stable Yang-Mills fields on spheres.

Let $F: [0, \infty) \to [0, \infty)$ be a strictly increasing $C^2$ function with $F(0)=0$. We unify the concepts of $F$-harmonic maps, minimal hypersurfaces, maximal spacelike hypersurfaces, and Yang-Mills Fields, and introduce $F$-Yang-Mills fields, $F$-degree, $F$-lower degree, and generalized Yang-Mills-Born-Infeld…

Study wormholes in Einstein-Yang-Mills theory with a phantom field.

We study pseudo Yang-Mills fields on a compact strictly pseudoconvex CR manifold.

Proves existence of Yang-Mills fields for specific curvature conditions.

Researchers can retrieve Yang-Mills-Higgs fields from Minkowski space measurements.

Utilizing a number of results of Dittmann, we investigate the nature of the Yang-Mills field over the eight-dimensional convex set, endowed with the Bures metric, of three-level quantum systems. Adopting a numerical strategy, we first decompose the field into self-dual and anti-self-dual components, by implementing the…

Proves local existence and extension principle for Einstein Yang--Mills system with spherical symmetry.

Explains Uhlenbeck's work on maps and fields.

Smooth Yang-Mills fields proved in supercritical dimensions.

Study on Yang-Mills fields blow-up in 4D, proving certain configurations impossible.

Study generalizes Yang-Mills equations for special complex surfaces.

In this paper, we introduce some notions on the pair consisting of a Chern connection and a Higgs field closely related to the first and second variation of Yang-Mills- Higgs functional, such as strong Yang-Mills-Higgs pair, degenerate Yang-Mills-Higgs pair, stable Yang-Mills-Higgs pair. We investigate some properties …

Extends weak continuity of Yang-Mills connections to a broader class.

Study Yang-Mills connections on four-manifolds, derive obstructions to bubbling.

Study of Yang-Mills fields on 4-manifolds using modified Lévy Laplacians.

The paper defines and analyzes higher-order Yang-Mills-Higgs functionals and their gradient flows.

A framework for constructing new kinds of gauge theories is suggested. Essentially it consists in replacing Lie algebras by Lie or Courant algebroids. Besides presenting novel topological theories defined in arbitrary spacetime dimensions, we show that equipping Lie algebroids E with a fiber metric having sufficiently …

We study isolated singularities of two dimensional Yang-Mills-Higgs fields defined on a fiber bundle, where the fiber space is a compact Riemannian manifold and the structure group is a compact connected Lie group. In general the singularity can not be removed due to possibly non-vanishing limit holonomy around the sin…

In the context of D-dimensional Euclidean gravity, we define the natural generalisation to D-dimensions of the self-dual Yang-Mills equations, as duality conditions on the curvature 2-form of a Riemannian manifold. Solutions to these self-duality equations are provided by manifolds of SU(2), SU(3), G_2 and Spin(7) holo…

The gradient flow of the Yang-Mills action acts pointwise on closed loops of gauge fields. We construct a topologically nontrivial loop of SU(2) gauge fields on S4 that is locally stable under the flow. The stable loop is written explicitly as a path between two gauge fields equivalent under a topologically nontrivial …

Classifications of all biharmonic isoparametric hypersurfaces in the unit sphere, and all biharmonic homogeneous real hypersurfaces in the complex or quaternionic projective spaces are shown. Answers in case of bounded geometry to Chen's conjecture or Caddeo, Montaldo and Piu's one on biharmonic maps into a manifold of…

The paper examines Yang-Mills-Higgs pairs on vector bundles and proves stability and energy identity.

Study investigates singularity formation in $\alpha$-Yang-Mills-Higgs fields on spheres.

Lie algebroid Yang-Mills theories are a generalization of Yang-Mills gauge theories, replacing the structural Lie algebra by a Lie algebroid E. In this note we relax the conditions on the fiber metric of E for gauge invariance of the action functional. Coupling to scalar fields requires possibly nonlinear representatio…

Stability of singularity formation in Yang-Mills fields in higher dimensions.

We prove an $L^{2}$ energy gap result for Yang-Mills connections on principal $G$-bundles over compact Kähler surfaces with positive scalar curvature. We prove related results for compact simply-connected Calabi-Yau $2$-folds.

Using the results and techniques of a previous paper where we proved the quantization of gravity we extend the former result by adding a Yang-Mills functional and a Higgs term to the Einstein-Hilbert action.

We extend Eardley and Moncrief's $L^\infty$ estimates for the conformally invariant Yang-Mills-Higgs equations to the Einstein cylinder. Our method is to first work on Minkowski space and localise their estimates, and then carry them to the Einstein cylinder by a conformal transformation. By patching local estimates to…

This is an introductory chapter in a series in which we take a systematic study of the Yang-Mills equations on curved space-times. In this first, we provide standard material that consists in writing the proof of the global existence of Yang-Mills fields on arbitrary curved space-times using the Klainerman-Rodnianski p…

Characterizes a specific type of Courant algebroid with a Calabi-Yau structure.

In these lectures we review how the symmetries of gravitational theories may be regarded as originating from those of "Yang-Mills squared". We begin by motivating the idea that certain aspects of gravitational theories can be captured by the product, in some sense, of two distinct Yang-Mills theories, particularly in t…

In this paper, we study the convergence of Yang-Mills-Higgs fields defined on fiber bundles over Riemann surfaces where the fiber is a compact symplectic manifold and the conformal structure of the Riemann surface is allowed to vary. We show that away from the nodes, the YMH fields converges, up to gauge, to a smooth Y…

Stability of Morse index for Yang-Mills connections in 4D.

We show the existence of Yang--Mills--Higgs (YMH) fields over a Riemann surface with boundary where a free boundary condition is imposed on the section and a Neumann boundary condition on the connection. In technical terms, we study the convergence and blow-up behavior of a sequence of Sacks-Uhlenbeck type $α$-YMH fiel…

Develops a unified theory of Yang-Mills and GR using generalized principal bundles.

In this article, we study the analytical properties of the solutions of the complex Yang-Mills equations on a closed Riemannian four-manifold $X$ with a Riemannian metric $g$. The main result is that if $g$ is $good$ and the connection is an approximate ASD connection, then the extra field has a positive lower {bound}.…

The Levy Laplacian is studied on manifolds, with heat flow solutions tending to constant functionals over time.

Proposes a new gauge theory for fuzzy geometries using finite-dimensional algebras.

Proves stability of Minkowski space-time in Einstein-Yang-Mills system.