arXiv research

Study the deformation theory of Einstein-Yang-Mills system on compact manifolds.

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

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

Developed a new symmetric hyperbolic formulation for Einstein-Yang-Mills system.

In this paper, we prove a convergence theorem for sequences of Einstein Yang-Mills systems on $U(1)$-bundles over closed $n$-manifolds with some bounds for volumes, diameters, $L^{2}$-norms of bundle curvatures and $L^{\frac{n}{2}}$-norms of curvature tensors. This result is a generalization of earlier compactness the…

Stability of Minkowski space-time in higher dimensions proven for arbitrary small perturbations.

Introduces new equations linking Kähler-Einstein and Hermitian-Yang-Mills theories.

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

Stability of Minkowski space-time in Einstein-Yang-Mills system proven.

The paper explores Kaluza-Klein theories without assuming a fibration structure.

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

Compact formulas for Yang-Mills conditions on conformal manifolds.

Proves stability of Minkowski space-time for Einstein-Yang-Mills equations.

Study classifies Einstein-Yang-Mills spaces in 4D symmetric spaces.

Proves energy expression on Poincaré-Einstein spaces.

Let $P$ be a principal U(1)-bundle over a closed manifold $M$. On $P$, one can define a modified version of the Ricci flow called the Ricci Yang-Mills flow, due to these equations being a coupling of Ricci flow and the Yang-Mills heat flow. We use maximal regularity theory and ideas of Simonett concerning the asymptoti…

Study generalizes Yang-Mills equations for special complex surfaces.

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 full Yang-Mills equations. A special case is a complex controlling the deformation…

The paper finds explicit instantons on a specific 6-manifold.

Construct Hermitian-Einstein metrics on stable holomorphic vector bundles using dynamical methods.

The paper presents new formulations of gauge and gravity theories using dynamical principal bundles.

We prove a conformally invariant estimate for the index of Schrödinger operators acting on vector bundles over four-manifolds, related to the classical Cwikel-Lieb-Rozenblum estimate. Applied to Yang-Mills connections we obtain a bound for the index in terms of its energy which is conformally invariant, and captures th…

We provide non trivial examples of solutions to the system of coupled equations introduced by M. García-Fernández for the uniformization problem of a triple $(M,L,E)$ where $E$ is a holomorphic vector bundle over a polarized complex manifold $(M,L)$, generalizing the notions of both constant scalar curvature Kähler met…

New obstruction found for Hull-Strominger system solutions.

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…

A family of new twistor string theories is constructed and shown to be free from world-sheet anomalies. The spectra in space-time are calculated and shown to give Einstein supergravities with second order field equations instead of the higher derivative conformal supergravities that arose from earlier twistor strings. …

This review discusses solutions to Einstein's equations using twistor theory.

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 review aspects of twistor theory, its aims and achievements spanning thelast five decades. In the twistor approach, space--time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex three--fold -- the twistor space. After giving an elementary construction of this s…

We extend the conformal gluing construction of Isenberg-Mazzeo-Pollack [18] by establishing an analogous gluing result for field theories obtained by minimally coupling Einstein's gravitational theory with matter fields. We treat classical fields such as perfect fluids and the Yang-Mills equations as well as the Einste…

We study and construct non-abelian hermitian Yang-Mills (HYM) instantons on Calabi-Yau cones. By means of a particular isometry preserving ansatz, the HYM equations are reduced to a novel Higgs-Yang-Mills flow on the Einstein-Kahler base. For any 2d-dimensional Calabi-Yau cone, we find explicit solutions of the flow eq…

Study quantizes topological numbers on degenerating Einstein manifolds.

Study of deformed Hermitian Yang-Mills equations with variable Kähler metrics.

On a five dimensional simply connected Sasaki-Einstein manifold, one can construct Yang-Mills theories coupled to matter with at least two supersymmetries. The partition function of these theories localises on the contact instantons, however the contact instanton equations are not elliptic. It turns out that these equa…

We show how the well-known classical field equations as Einstein and Yang-Mills ones, which arise as the conformal invariance conditions of certain two-dimensional theories, expanded up to the second order in the formal parameter, can be reformulated as Generalized/formal Maurer-Cartan equations (GMC), where the differ…

We use an elliptic system of equations with complex coefficients for a set of complex-valued tensor fields as a tool to construct infinite-dimensional families of non-singular stationary black holes, real-valued Lorentzian solutions of the Einstein-Maxwell-dilaton-scalar fields-Yang-Mills-Higgs-Chern-Simons-$f(R)$ equa…

The Einstein/Abelian-Yang-Mills Equations reduce in the stationary and axially symmetric case to a harmonic map with prescribed singularities $\p\colon\R^3\smΣ\to\H^{k+1}_\C$ into the $(k+1)$-dimensional complex hyperbolic space. In this paper, we prove the existence and uniqueness of harmonic maps with prescribed sing…

Study on Yang-Mills equations on conformally compact manifolds, finding obstructions and asymptotics.

Study para-Kähler-Einstein metrics and their non-integrable twistor distributions.

In this paper we construct new solutions of the Kahler-Yang-Mills equations, by applying dimensional reduction methods to the product of the complex projective line with a compact Riemann surface. The resulting equations, that we call gravitating vortex equations, describe Abelian vortices on the Riemann surface with b…

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 …

New conformal geometry method solves Einstein-Weyl equations.

We construct Yang-Mills connections on SO(n)-bundles over spheres equipped with the Euclidean metric. We use a cohomogeneity one group action on the bundle to reduce the Yang-Mills-equation to a system of ordinary differential equations. The system is shown to have solutions by variational methods, using ideas from har…

Exterior differential systems are given, and their Cartan characters calculated, for Maxwell and SU(2)-Yang-Mills equations in dimensions from three to six.

Original abstract: "We construct periodic solutions of nonlinear wave equations using analytic continuation. The construction applies in particular to Einstein equations, leading to infinite-dimensional families of time-periodic solutions of the vacuum, or of the Einstein-Maxwell-dilaton-scalar fields-Yang-Mills-Higgs-…

A projective geometry is an equivalence class of torsion free connections sharing the same unparametrised geodesics; this is a basic structure for understanding physical systems. Metric projective geometry is concerned with the interaction of projective and pseudo-Riemannian geometry. We show that the BGG machinery of …

Study of 0-instantons on hyperbolic manifolds, proving invariants and energy formulas.

We consider SU(3)-equivariant dimensional reduction of Yang-Mills theory over certain cyclic orbifolds of the 5-sphere which are Sasaki-Einstein manifolds. We obtain new quiver gauge theories extending those induced via reduction over the leaf spaces of the characteristic foliation of the Sasaki-Einstein structure, whi…