Related papers: The Yang-Mills flow for cylindrical end 4-manifold…
This is a survey of recent studies of singularity formation in solutions of spherically symmetric Yang-Mills equations in higher dimensions. The main attention is focused on five space dimensions because this case exhibits interesting…
Under the validity of the positive mass theorem, the Yamabe flow on a smooth compact Riemannian manifold of dimension $N \ge 3$ is known to exist for all time $t$ and converges to a solution to the Yamabe problem as $t \to \infty$. We prove…
We construct d<=7 dimensional maximally supersymmetric Yang-Mills theories on a class of curved backgrounds with off-shell supercharges. The off-shell supersymmetry is mainly a generalization of on-shell supersymmetry constructed previously…
We present some of the latest results from our numerical investigations of N=4 supersymmetric Yang--Mills theory formulated on a space-time lattice. Based on a construction that exactly preserves a single supersymmetry at non-zero lattice…
We use the energy gap result of pure Yang-Mills equation [Feehan P.M.N., Adv. Math. 312 (2017), 547-587, arXiv:1502.00668] to prove another energy gap result of complex Yang-Mills equations [Gagliardo M., Uhlenbeck K., J. Fixed Point Theory…
In this paper we study the long time existence of the Ricci-harmonic flow in terms of scalar curvature and Weyl tensor which extends Cao's result \cite{Cao2011} in the Ricci flow. In dimension four, we also study the integral bound of the…
In this paper we study on-shell diagrams in ${\cal N}{<}4$ supersymmetric Yang-Mills (SYM) theory. These are on-shell gauge invariant objects which appear as cuts of loop integrands in the context of generalized unitarity and serve as…
We propose a SymTFT for 4d $U(N)$ Yang-Mills theory and its variants. We show that the SymTFT reproduces the structure of the global one-form symmetry in these theories. We consider the holographic embedding of this SymTFT, and observe that…
The use of gauged ${\cal N} = 8$ supergravity as a tool in studying the AdS/CFT correspondence for ${\cal N} = 4$ Yang-Mills theory is reviewed. The supergravity potential implies a non-trivial, supersymmetric IR fixed point, and the flow…
We geometrically engineer d=4 N=1 supersymmetric Yang-Mills theories by considering M theory on various Joyce orbifolds. We argue that the superpotential of these models is generated by fractional membrane instantons. The relation of this…
We consider the Yang-Mills flow equations on a reductive coset space G/H and the Yang-Mills equations on the manifold R x G/H. On nonsymmetric coset spaces G/H one can introduce geometric fluxes identified with the torsion of the spin…
We introduce the gradient flow of the Seiberg-Witten functional on a compact, orientable Riemannian 4-manifold and show the global existence of a unique smooth solution to the flow. The flow converges uniquely in $C^\infty$ up to gauge to a…
We consider the unnormalized Yamabe flow on manifolds with conical singularities. Under certain geometric assumption on the initial cross-section we show well posedness of the short time solution in the $L^q$-setting. Moreover, we give a…
We review how (dimensionally regulated) scattering amplitudes in N=4 super-Yang-Mills theory provide a useful testing ground for perturbative QCD calculations relevant to collider physics, as well as another avenue for investigating the…
We generalize the gradient flow equation for field theories with nonlinearly realized symmetry. Applying the formalism to super Yang-Mills theory, we construct a supersymmetric extension of the gradient flow equation. It can be shown that…
We show the existence of infinitely many geometrically distinct homothetic expanders (jellyfish) for the elastic flow, epicyclic shrinkers for the curve diffusion flow, and epicyclic expanders for the ideal flow.
We establish the short-time existence of the Ricci flow on surfaces with a finite number of conic points, all with cone angle between 0 and $2\pi$, where the cone angles remain fixed or change in some smooth prescribed way. For the…
The rigorous construction of quantum Yang-Mills theories, especially in dimension four, is one of the central open problems of mathematical physics. Construction of Euclidean Yang-Mills theories is the first step towards this goal. This…
Chen's flow is a fourth-order curvature flow motivated by the spectral decomposition of immersions, a program classically pushed by B.-Y. Chen since the 1970s. In curvature flow terms the flow sits at the critical level of scaling together…
We consider the surface diffusion and Willmore flows acting on a general class of (possibly non-compact) hypersurfaces parameterized over a uniformly regular reference manifold possessing a tubular neighborhood with uniform radius. The…