Related papers: The Yang-Mills flow for cylindrical end 4-manifold…

We describe some recent progress in our understanding of Yang-Mills theories formulated on noncommutative spaces and in particular how to formulate the standard model on such spaces.

In this paper, we prove a unique continuation or ``backwards-uniqueness'' theorem for solutions to the Ricci flow. A particular consequence is that the isometry group of a solution cannot expand within the lifetime of the solution.

The Euclidean version of Yang-Mills theory coupled to a massive dilaton is investigated. Our analytical and numerical results imply existence of infinite number of branches of globally regular, spherically symmetric, dyonic type solutions…

In this proceedings contribution we will review the main ideas behind the many recent works that apply the gradient flow to the determination of the renormalized coupling and the renormalization of composite operators. We will pay special…

We study the gradient flow lines of a Yang-Mills-type functional on the space of gauged holomorphic maps $\mathcal{H}(P,X)$, where $P$ is a principal bundle on a Riemann surface $\Sigma$ and $X$ is a K\"ahler Hamiltonian $G$-manifold. For…

This is an exposition of the Donaldson geometric flow on the space of symplectic forms on a closed smooth four-manifold, representing a fixed cohomology class. The original work appeared in [1].

Taubes' gluing theorems establish the existence of ASD connections on closed, oriented 4-manifolds. We extend these gluing results to the mASD connections of Morgan-Mrowka-Ruberman on oriented 4-manifolds with cylindrical ends. As a…

We formulate maximally supersymmetric Yang-Mills theory in five dimensions in light-cone superspace. The light-cone Hamiltonian is of the quadratic form and the theory can be understood as an oxidation of the N=4 Super Yang-Mills Theory in…

We present evidence that loop amplitudes in maximally supersymmetric $\mathcal{N}=4$ Yang-Mills (SYM) beyond the planar limit share some of the remarkable structures of the planar theory. In particular, we show that through two loops, the…

We consider applications of the theory of balanced weight filtrations and iterated logarithms, initiated in arXiv:1706.01073, to PDEs. The main result is a complete description of the asymptotics of the Yang--Mills flow on the space of…

In this paper we consider $4$-dimensional steady soliton singularity models, i.e., complete steady gradient Ricci solitons that arise as the rescaled limit of a finite time singular solution of the Ricci flow on a closed $4$-manifold. In…

We calculate the collinear anomalous dimensions in massless four-loop QCD and $\mathcal{N} = 4$ supersymmetric Yang-Mills theory from the infrared poles of vertex form factors. We give very precise numerical approximations and a conjecture…

We consider topologically twisted N=4 supersymmetric Yang-Mills theory on a four-manifold of the form V = W \times R_+ or V = W \times I, where W is a Riemannian three-manifold. Different kinds of boundary conditions apply at infinity or at…

We survey some recent developments on solutions of the K\"ahler-Ricci flow on compact K\"ahler manifolds which exist for all positive times.

For gauge groups SO$(n{+}1)$, SU$(m{+}1)$ and Sp$(\ell{+}1)$, we construct equivariant Yang-Mills solutions on de Sitter space in $n{+}1$, $2(m{+}1)$ and $4(\ell{+}1)$ spacetime dimensions. The latter is conformally mapped to a finite…

We initiate the study of a new nonlinear parabolic equation on a Riemann surface. The evolution equation arises as a reduction of the Anomaly flow on a fibration. We obtain a criterion for long-time existence for this flow, and give a range…

We study the long time behavior of the Hesse-Koszul flow on compact Hessian manifolds. When the first affine Chern class is negative, we prove that the flow converges to the unique Hesse-Einstein metric. We also derive a convergence result…

We consider a spherically symmetric (magnetic) $SU(2)$ Yang-Mills field propagating on the exterior of the extremal Reissner-Nordstr\"om black hole. Taking advantage of the conformal symmetry, we reduce the problem to the study of the…

The spectrum of D=4 supersymmetric Yang-Mills quantum mechanics is computed with high accuracy in all channels of angular momentum and fermion number. Localized and non-localized states coexists in certain channels as a consequence of the…

We compute the Large N limit of several objects related to the two-dimensional Euclidean Yang-Mills measure on compact connected orientable surfaces of genus larger or equal to one, with a structure group taken among the classical groups of…