Related papers: Energy Quantization for Yamabe's problem in Confor…

A recent investigation of SU(2) Yang-Mills theory found several classical solutions with bad behaviour at infinity : one of the potential components oscillated and another tended to infinity. In this paper we apply an idea due to Heisenberg…

In conformal geometry, the Compactness Conjecture asserts that the set of Yamabe metrics on a smooth, compact, aspherical Riemannian manifold (M,g) is compact. Established in the locally conformally flat case by Schoen [43,44] and for n\leq…

In this paper, we study the blow-up of a sequence of Yang-Mills connection with bounded energy on a four manifold. We prove a set of equations relating the geometry of the bubble connection at the infinity with the geometry of the limit…

For a simply connected closed Riemannian manifold with positive scalar curvature, we prove an upper diameter bound in terms of its scalar curvature integral, the Yamabe constant and the dimension of the manifold. When a manifold has a…

The radiative correction to beta function is comprehensively studied at 1 loop in the context of universal extra dimensions. Instead of using cutoffs to regularize 1-loop divergences, the dimensional regularization scheme is used. Large…

We suggest a new generalization of the $\mathrm{U}(n)$ Yang-Mills theory obtained by relaxing the condition of covariant constancy of the Hermitian form in the fibers, $\nabla_a g_{\alpha\beta'} \ne 0$. This theory is a simpler analogue of…

We study the perturbation expansion of the free energy of N=4 supersymmetric SU(N) Yang-Mills at finite temperature in powers of 't Hooft's coupling g^2 N in the large N limit. Infrared divergences are controlled by constructing a hierarchy…

We present a compact formula, expressed in terms of classical polylogarithms up to weight three, for the leading order four-point energy correlator in maximally supersymmetric Yang-Mills theory, in the limit where the four detectors are…

A mathematically rigorous relativistic quantum Yang-Mills theory with an arbitrary semisimple compact gauge Lie group is set up in the Hamiltonian canonical formalism. The theory is non-perturbative, without cut-offs, and agrees with the…

Two classes of observables defined on the configuration space of a particle are quantized, and the effects of the Yang-Mills field are discussed in the context of geometric quantization.

Let $(M, g)$ be a compact Riemannian manifold with boundary. The Yamabe problem concerning the existence of a metric conformally equivalent to $g$ having constant scalar curvature on $M$ and constant mean curvature on its boundary is…

We investigate the blow-up behavior of sequences of sign-changing solutions for the Yamabe equation on a Riemannian manifold $(M,g)$ of positive Yamabe type. For each dimension $n\ge11$, we describe the value of the minimal energy threshold…

We start by taking the analytical approach to discuss how the minimizer of Yamabe functional provides constant scalar curvature and its relationship with the Sobolev Space $W^{1,2}.$ Then, after demonstrating the importance of the sphere…

In two dimensions a large class of gravitational systems including, e.g., $R^2$-gravity can be quantized exactly also when coupled dynamically to a Yang-Mills theory. Some previous considerations on the quantization of pure gravity theories…

We study the Yamabe equation in the Euclidean half-space. We prove that any sign-changing solution has at least twice the energy of a standard bubble. Moreover, a sharper energy lower bound of the sign-changing solution set is also…

We show how to formulate Yang-Mills Theory in \m{2+1} dimensions as a hamitonian system within a simplicial regularization and construct its quantization, with special attention to the mass gap. An approximate conformal invariance of the…

The space of Sobolev connections, as it has been introduced for studying the variation of Yang-Mills Lagrangian in the critical dimension $4$, happens not to be weakly sequentially complete in dimension larger than $4$. This is a major…

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…

A recent investigation of the SU(3) Yang-Mills field equations found several classical solutions which exhibited a type of confinement due to gauge fields which increased without bound as $r \to \infty$. This increase of the gauge fields…

We consider the ambitwistor description of $\mathcal N$=4 supersymmetric extension of U($N$) Yang-Mills theory on Minkowski space $\mathbb R^{3,1}$. It is shown that solutions of super-Yang-Mills equations are encoded in real analytic…