arXiv research

The paper studies how adding a 'Gauge Mass' term breaks gauge symmetry in Yang-Mills-Higgs systems and analyzes the resulting behavior.

The paper studies minimal submanifolds from the abelian Higgs model, proving convergence of energy measures and currents.

The paper shows how Yang-Mills-Higgs energies converge to the $(n-2)$-area functional.

The paper proves unique blow-down for critical points of a Yang-Mills-Higgs functional.

Study on vortex sheet formation in Abelian gauge theories.

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

Study bounds the index of minimal submanifolds using energy measures and Yang-Mills-Higgs equations.

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

Integrability of the (2+1)-dimensional Gauss-Codazzi-Mainardi equation is considered. It is shown that this equation is the particular cases of the Yang-Mills-Higgs-Bogomolny and self-dual Yang-Mills equations.

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

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

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

The study finds critical points of Yang-Mills-Higgs energy on 3-manifolds.

We prove an energy identity for anti-self-dual connections on the product C\timesΣof the complex plane and a Riemann surface. The energy is a multiple of a basic constant that is determined from the values of a corresponding Chern-Simons functional on flat connections and its ambiguity under gauge transformations. For …

Reformulates binary classification on manifolds using Yang-Mills-Higgs theory.

In this paper we consider $\rm SU(2)$ monopoles on an asymptotically conical, oriented, Riemannian $3$-manifold with one end. The connected components of the moduli space of monopoles in this setting are labeled by an integer called the charge. We analyse the limiting behavior of sequences of monopoles with fixed charg…

We investigate monotonicity properties of $p$-harmonic vector bundle-valued $k$-forms by studying the energy-momentum tensor associated with such a form. As a consequence, we obtain a unified proof of the monotonicity formulæ for $p$-harmonic maps and Yang-Mills connections, proving a monotonicity formula for $p$-Yang-…

Study on finite energy SU(2) monopoles on AC 3-manifolds, proving integrality of charge and curvature decay.

The paper studies a geometric model combining Kaluza-Klein, Yang-Mills, and Dirac actions.

Weyl energy decreases for connected sums of certain four-manifolds.

Study examines Yang-Mills-Higgs energy convergence to codimension-three area functional.

We generalize our previous results (Theorem 1 and Corollary 2 in arXiv:1412.4114) and Theorem 1 in arXiv:1502.00668) on the existence of an $L^2$-energy gap for Yang-Mills connections over closed four-dimensional manifolds and energies near the ground state (occupied by flat, anti-self-dual, or self-dual connections) t…

We develop a new method for proving regularity for small energy stationary solutions of coupled gauge field equations. Our results duplicate those of Tian--Tao [7] for the pure Yang Mills equations, but our proof is simpler, and obtains bounded curvature without the use of Coulomb gauges. It relies instead on the Weitz…

Minimal submanifolds are found as energy concentration sets in variational problems.

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…

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 …

We investigate Yang--Mills instanton theory over four dimensional asymptotically locally flat (ALF) geometries, including gravitational instantons of this type, by exploiting the existence of a natural smooth compactification of these spaces introduced by Hausel--Hunsicker--Mazzeo. First referring to the codimension 2 …

Growth of spinors in 4D and 3D generalized Seiberg-Witten equations.

Several results on existence and convergence of the Yang-Mills flow in dimension four are given. We show that a singularity modeled on an instanton cannot form within finite time. Given low initial self-dual energy, we then study convergence of the flow at infinite time. If an Uhlenbeck limit is anti-self-dual and has …

Stable solutions to Yang-Mills-Higgs equations on spheres and tori identified.

Compact theorem for $SO(3)$ anti-self-dual equations on cylindrical manifolds.

New metric reduces Weyl's energy in manifold connected sums.

Sharp decay estimate for Yang-Mills-Higgs fields near singular points.

A local monotonicity formula for the Yang-Mills-Higgs flow on $G$-bundles over $\mathbb{R}^{n}$ ($n>4$) is proved. It is shown that the monotone quantity coïncides on certain self-similar solutions with that appearing in existing non-local monotonicity formulæ for the Yang-Mills and Yang-Mills-Higgs flows.

Paper studies convergence of Yang-Mills-Higgs flow on Kähler manifolds.

Extends decay estimates for Yang-Mills-Higgs fields on Minkowski and de Sitter spacetimes.

In this note we address the problem of finding Abelian instantons of finite energy on the Euclidean Schwarzschild manifold. This amounts to construct self-dual L^2 harmonic 2-forms on the space. Gibbons found a non-topological L^2 harmonic form in the Taub-NUT metric, leading to Abelian instantons with continuous energ…

Let $X$ be a compact connected Kähler--Einstein manifold with $c_1(TX)\, \geq\, 0$. If there is a semistable Higgs vector bundle $(E\,,θ)$ on $X$ with $θ\,\not=\,0$, then we show that $c_1(TX)=0$, any $X$ satisfying this condition is called a Calabi--Yau manifold, and it admits a Ricci--flat Kähler form \cite{Ya}. Let …

In this paper, we consider the gradient flow of the Yang-Mills-Higgs functional for Higgs pairs on a Hermitian vector bundle $(E, H_{0})$ over a compact Kähler manifold $(M, ω)$. We study the asymptotic behavior of the Yang-Mills-Higgs flow for Higgs pairs at infinity, and show that the limiting Higgs sheaf is isomorph…

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

Let (E, \varphi) be a flat Higgs bundle on a compact special affine manifold M equipped with an affine Gauduchon metric. We prove that (E, \varphi) is polystable if and only if it admits an affine Yang-Mills-Higgs metric.

Stable solutions found for a specific physics model.

New flow for Yang-Mills-Higgs theory avoids singularities.

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

For any compact Lie group $G$ and closed, smooth Riemannian manifold $(X,g)$ of dimension $d\geq 2$, we extend a result due to Uhlenbeck (1985) that gives existence of a flat connection on a principal $G$-bundle over $X$ supporting a connection with $L^p$-small curvature, when $p>d/2$, to the case of a connection with …

Study vortices in Kähler-Yang-Mills equations on complex manifolds.

A self-dual harmonic 2-form on a 4-dimensional Riemannian manifold is symplectic where it does not vanish. Furthermore, away from the form's zero set, the metric with the 2-form give a compatible almost complex structure and thus pseudo-holomorphic subvarieties. Such a subvariety is said to have finite energy when the …

The study proves constraints on the structure of compact half-conformally flat manifolds.