Related papers: Sharp estimate of global Coulomb gauge

We consider F-theory and M-theory compactifications on singular Calabi-Yau fourfolds with an SU(5) singularity. On the M-theory side this realizes three-dimensional N=2 supersymmetric gauge theories with matter, and compactification on a…

In a recent work, it has been pointed out that certain observables of the massless scalar field theory in a static spherically symmetric background exhibit a universal behavior at large distances. More precisely, it was shown that, unlike…

We extend an $L^2$ energy gap result due independently to Min-Oo and Parker (1982) for Yang-Mills connections on principal $G$-bundles, $P$, over closed, connected, four-dimensional, oriented, smooth manifolds, $X$, from the case of…

It is believed that any classical gauge symmetry gives rise to an L$_\infty$ algebra. Based on the recently realized relation between classical ${\cal W}$ algebras and L$_\infty$ algebras, we analyze how this generalizes to the quantum…

The paper is devoted to provide Michael-Simon-type $L^p$-logarithmic-Sobolev inequalities on complete, not necessarily compact $n$-dimensional submanifolds $\Sigma$ of the Euclidean space $\mathbb R^{n+m}$. Our first result, stated for…

Let $\mathcal{C}(\mathcal{R},n,p,\Lambda,D,V_0)$ be the class of compact $n$-dimensional Riemannian manifolds with finite diameter $\leq D$, non-collapsing volume $\geq V_0$ and $L^p$-bounded $\mathcal{R}$-curvature condition…

Let $(M,g)$ be a compact $n$-dimensional Riemannian manifold without boundary and $e_\lambda$ be an $L^2$-normalized eigenfunction of the Laplace-Beltrami operator with respect to the metric $g$, i.e \[ -\Delta_g e_\lambda = \lambda^2…

Recently Alday, Gaiotto and Tachikawa proposed a conjecture relating 4-dimensional super-symmetric gauge theory for a gauge group G with certain 2-dimensional conformal field theory. This conjecture implies the existence of certain…

In this paper, we introduce a new energy density function $\mathscr Y$ on the projective bundle $\mathbb{P}(T_M)\>M$ for a smooth map $f:(M,h)\>(N,g)$ between Riemannian manifolds $$\mathscr Y=g_{ij}f^i_\alpha f^j_\beta \frac{W^\alpha…

Let $(M^{n}, g)$ be a closed connected Einstein space, $n=dim M ,$ and $\kappa_{0} $ be the lower bound of the sectional curvature. In this paper, we prove Udo Simon's conjecture: on closed Einstein spaces, $n\geq 3,$ there is no eigenvalue…

For a noncommutative algebra $\mathcal{A}$ and an antilinear automorphism $\rho$ of $\mathcal{A}$, there is a notion of a positive trace. When we have a three-dimensional $\mathcal{N}=4$ gauge theory or four-dimensional $\mathcal{N}=2$…

In this paper we prove two approximation results for divergence free measures. The first is a form of an assertion of J. Bourgain and H. Brezis concerning the approximation of solenoidal charges in the strict topology: Given $F \in…

We establish some sharp weighted trace inequalities $W^{1,2}(\rho^{1-2\sigma}, M)\hookrightarrow L^{\frac{2n}{n-2\sigma}}(\pa M)$ on $n+1$ dimensional compact smooth manifolds with smooth boundaries, where $\rho$ is a defining function of…

Obtaining the classification of 3d $\mathcal{N}=4$ quivers whose Coulomb branches have an isolated singularity is an essential step in understanding moduli spaces of vacua of supersymmetric field theories with 8 supercharges in any…

Let $(M, g)$ be a closed Riemannian manifold of dimension $5$. Assume that $(M, g)$ is not conformally equivalent to the round sphere. If the scalar curvature $R_g\geq 0$ and the $Q$-curvature $Q_g\geq 0$ on $M$ with $Q_g(p)>0$ for some…

We compute instanton corrections to correlators in the genus-zero topological subsector of a (0,2) supersymmetric gauged linear sigma model with target space P1xP1, whose left-moving fermions couple to a deformation of the tangent bundle.…

We resolve the problem of optimal regularity and Uhlenbeck compactness for affine connections in General Relativity and Mathematical Physics. First, we prove that any affine connection $\Gamma$, with components $\Gamma \in L^{2p}$ and…

We extend the results and methods of \cite{MP} to prove the existence of constant positive scalar curvature metrics $g$ which are complete and conformal to the standard metric on $S^N \setminus \Lambda$, where $\Lambda$ is a disjoint union…

In this paper we provide a \emph{global} investigation of the geometry of parallelizable manifolds (or absolute parallelism geometry) frequently used for application. We discuss the different linear connections and curvature tensors from a…

We describe the self-duality symmetries for 4d Maxwell theory at any value of the coupling $\tau$ via topological manipulations that include gauging continuous symmetries with flat connections. Moreover, we demonstrate that the…