Related papers: The stability for F-Yang-Mills functional on CP^n

We investigate hermitian Yang-Mills connections on pullback bundles with respect to adiabatic classes on the total space of holomorphic submersions with connected fibres. Under some technical assumptions on the graded object of a…

In this paper we introduce entropy-stability and F-stability for homothetically shrinking Yang-Mills solitons, employing entropy and second variation of $\mathcal{F}$-functional respectively. For a homothetically shrinking soliton which…

Consider a Yang-Mills connection over a Riemann manifold $M=M^n$, $n\ge 3$, where $M$ may be compact or complete. Then its energy must be bounded from below by some positive constant, if $M$ satisfies certain conditions, unless the…

We consider the Yang-Mills (YM) QFT with group $U(N)$. We take a finite lattice regularization $\Lambda\subset a\mathbb Z^d$, $d = 2,3,4$, with $a\in (0,1]$ and $L$ (even) sites on a side. Each bond has a gauge variable $U\in U(N)$. The…

In this paper, we provide the notions of connection $1$-forms and curvature $2$-forms on graphs. We prove a Weitzenb\"ock formula for connection Laplacians in this setting. We also define a discrete Yang-Mills functional and study its…

We write a gravity theory with Yang-Mills type action using the biconformal gauging of the conformal group. We show that the resulting biconformal Yang-Mills gravity theories describe 4-dim, scale-invariant general relativity in the case of…

Given a principal bundle on an orientable closed surface with compact connected structure group, we endow the space of based gauge equivalence classes of smooth connections relative to smooth based gauge transformations with the structure…

Yang-Mills gravity with translational gauge group T(4) in flat space-time implies a simple self-coupling of gravitons and a truly conserved energy-momentum tensor. Its consistency with experiments crucially depends on an interesting…

In "The Yang-Mills equations over Riemann surfaces", Atiyah and Bott studied Yang-Mills functional over a Riemann surface from the point of view of Morse theory. We generalize their study to all closed, compact, connected, possibly…

In this paper, we study the Yang-Mills functional on quantum Heisenberg manifolds using the appratuses developed by A. Connes and M. Rieffel. It is discovered that a connection on a projective module over a quantum Heisenberg manifold is a…

We consider a vector bundle $E$ over a compact Riemannian manifold $M$=$M^{n}$,$n\geq 4$,and $A$ is a Yang-Mills connection with $L^{\frac{n}{2}}$ curvature $F_{A}$ on $E$.Then we prove a mean value inequality for the density…

This doctoral work deals with the analysis of some Yang-Mills solutions on 4-dimensional de Sitter space d$S_4$. The conformal equivalence of this space with a finite Lorentzian cylinder over the 3-sphere and also with parts of Minkowski…

We consider the $2+1$ dimensional Yang-Mills theory with gauge group $\text{SU}(N)$ on a flat 2-torus under twisted boundary conditions. We study the possibility of phase transitions (tachyonic instabilities) when $N$ and the volume vary…

The analysis of (2+1)-dimensional Yang-Mills ($YM_{2+1})$ theory via the use of gauge-invariant matrix variables is reviewed. The vacuum wavefunction, string tension, the propagator mass for gluons, its relation to the magnetic mass for…

We examine the phenomena of the chromomagnetic gluon condensation in the Yang-Mills theory and the problem of stability of the chromomagnetic vacuum fields. The apparent instability of the chromomagnetic vacuum fields is a result of…

We perform a lattice calculation of the Schr\"odinger functional running coupling in SU(2) Yang-Mills theory with six massless Wilson fermions in the fundamental representation. The aim of this work is to determine whether the above theory…

We study four dimensional large-N SU(N) Yang-Mills theory coupled to adjoint overlap fermions on a single site lattice. Lattice simulations along with perturbation theory show that the bare quark mass has to be taken to zero as one takes…

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 report recent results and developments from our ongoing lattice studies of $\mathcal N = 4$ supersymmetric Yang--Mills theory. These include a proof that only a single fine-tuning needs to be performed, so long as the moduli space is not…

Three-dimensional Yang-Mills theory allows for a deformation quadratic in the field strengths which can not be integrated to a local action without auxiliary fields. Yet, its covariant divergence consistently vanishes after iterating the…