相关论文: Gravitating vortices, cosmic strings, and the K\"a…
In this work we consider the gravitating vortex equations. These equations couple a metric over a compact Riemann surface with a hermitian metric over a holomorphic line bundle equipped with a fixed global section --- the Higgs field ---,…
We introduce the notion of twisted gravitating vortex on a compact Riemann surface. If the genus of the Riemann surface is greater than 1 and the twisting forms have suitable signs, we prove an existence and uniqueness result for suitable…
We present globally regular vortex-type solutions for a pure SU(2) Yang-Mills field coupled to gravity in 3+1 dimensions. These gravitating vortices are static, cylindrically symmetric and purely magnetic, and they support a non-zero…
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…
The K\"ahler-Yang-Mills equations are coupled equations for a K\"ahler metric on a compact complex manifold and a connection on a complex vector bundle over it. After briefly reviewing the main aspects of the geometry of the…
We consider vortex-type solutions in $d=5$ dimensions of the Einstein gravity coupled to a nonabelian SU(2) field posessing a nonzero electric part. After the dimensional reduction, this corresponds to a $d=4$…
We undertake a novel approach to the existence problem for gravitating vortices on a Riemann surface based on symplectic reduction by stages, which seems to be new in the PDE as well as the gauge theory literature. The main technical tool…
The Abelian Higgs model on a compact Riemann surface \Sigma of genus g is considered. We show that for g > 1 the Bogomolny equations for multi-vortices at critical coupling can be obtained as compatibility conditions of two linear equations…
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…
We give a complete solution to the existence problem for gravitating vortices with non-negative topological constant $c \geqslant 0$. Our first main result builds on previous results by Yang and establishes the existence of solutions to the…
We examine the metric of an isolated self-gravitating abelian-Higgs vortex in dilatonic gravity for arbitrary coupling of the vortex fields to the dilaton. We look for solutions in both massless and massive dilaton gravity. We compare our…
The Abelian Higgs model with or without external particles is considered in curved space. Using the dual transformation, we rewrite the model in terms of dual gauge fields and derive the Bogomol'nyi-type bound. We examine cylindrically…
The approach of metric-affine gravity initially distinguishes it from Einstein's general relativity. Using an independent affine connection produces a theory with 10+64 unknowns. We write down the Yang-Mills action for the affine connection…
This is a short review of classical solutions with gravitating Yang-Mills fields in $D>4$ spacetime dimensions. The simplest SO(4) symmetric particlelike and SO(3) symmetric vortex type solutions in the Einstein-Yang-Mills theory in D=5 are…
We derive the Bogomol'nyi equations in generalized Abelian Higgs theories which allow the coexistence of vortices and antivortices over a compact Riemann surface or the full plane. In the compact surface situation, we obtain a necessary and…
We study the classical solutions of the Einstein-Yang-Mills model in five dimensions in the presence of a cosmological constant $\Lambda$. Using a spherically symmetric ansatz and assuming that the fields do not depend on the extra…
The coupled Einstein-Yang-Mills equations on a time dependent axially symmetric spacetime are investigated, without a priori any conditions on the gauge field. There is numerical evidence for the existence of a regular solution with the…
A particular dimensional reduction of SU(2N) Yang--Mills theory on $\Sigma \times S^2$, with $\Sigma$ a Riemann surface, yields an $S(U(N) \times U(N))$ gauge theory on $\Sigma$, with a matrix Higgs field. The SU(2N) self-dual Yang--Mills…
There has been considerable interest in the possible cosmic string configurations and Y. Yang has recently derived intriguing obstructions to the existence of cylindrically symmetric solutions in the Bogomol'nyi critical phase of the…
We produce examples of solutions to the non-abelian gravitating vortex equations, which are a dimensional reduction of the K\"aher-Yang-Mills- Higgs equations. These are equations for a K\"ahler metric and a metric on a vector bundle. We…