Related papers: Single copy of the Ricci flow
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…
In this paper we study the global behavior of the Ricci flow equation for two classes of homogeneous manifolds with two isotropy summands. Using methods of the qualitative theory of differential equations, we present the global phase…
In this note, we provide some general discussion on the two main versions in the study of Kahler-Ricci flows over closed manifolds, aiming at smooth convergence to the corresponding Kahler-Einstein metrics with assumptions on the volume…
Two distinct gauge potentials can have the same field strength, in which case they are said to be ``copies'' of each other. The consequences of this possibility for the general space A of gauge potentials are examined. Any two potentials…
The Ricci iteration is a discrete analogue of the Ricci flow. We give the first study of the Ricci iteration on a class of Riemannian manifolds that are not K\"ahler. The Ricci iteration in the non-K\"ahler setting exhibits new phenomena.…
In [8], the gradient conjecture of R. Thom was proven for gradient flows of analytic functions on Rn. This result means that the secant at a limit point converges, so that the flow cannot spiral forever. Once the trajectory becomes…
We prove that monotonicity of density and energy inequality imply the rectifiability of the singular sets for Yang-Mills flow.
Given $\Bbb R^2, $ with a ``good'' complete metric, we show that the unique solution of the Ricci flow approaches a soliton at time infinity. Solitons are solutions of the Ricci flow, which move only by diffeomorphism. The Ricci flow on…
Double copy relates scattering amplitudes in a web of gravitational and gauge theories. Although it has seen great success when applied to amplitudes in vacuum, far less is known about double copy in arbitrary gravitational and gauge…
This paper investigates the question of stability for a class of Ricci flows which start at possibly non-smooth metric spaces. We show that if the initial metric space is Reifenberg and locally bi-Lipschitz to Euclidean space, then two…
We study the Ricci flow out of spaces with edge type conical singularities along a closed, embedded curve. Under the additional assumption that for each point of the curve, our space is locally modelled on the product of a fixed positively…
We prove the uniqueness of solutions of the Ricci flow on complete noncompact manifolds with bounded curvatures using the De Turck approach. As a consequence we obtain a correct proof of the existence of solution of the Ricci harmonic flow…
We discuss static axially symmetric solutions of SU(2) Einstein-Yang-Mills-Higgs theory for large scalar coupling. These regular asymptotically flat solutions represent monopole-antimonopole chain and vortex ring solutions, as well as new…
In a previous paper we observed that (classical) tree-level gauge theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory…
We study geodesics flows on curved quantum Riemannian geometries using a recent formulation in terms of bimodule connections and completely positive maps. We complete this formalism with a canonical $*$ operation on noncommutative vector…
We lay the foundations of a Morse homology on the space of connections on a principal $G$-bundle over a compact manifold $Y$, based on a newly defined gauge-invariant functional $\mathcal J$. While the critical points of $\mathcal J$…
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 formulate and explore the physical implications of a new translation gauge theory of gravity in flat space-time with a new Yang-Mills action, which involves quadratic gauge curvature and fermions. The theory shows that the presence of an…
We prove a sharp convergence theorem for the Yang-Mills flow on an $\mathrm{S}\mathrm{U}(r)$-bundle over a locally hyperK\"ahler ALE 4-manifold. Our main result is a noncompact version of the "parabolic gap theorem" previously established…
We consider quantized Yang-Mills theories in the framework of causal perturbation theory which goes back to Epstein and Glaser. In this approach gauge invariance is expressed by a simple commutator relation for the S-matrix. The most…