Asymptotic freedom of Yang–Mills theory with gravity

We study the behaviour of Yang–Mills theory under the inclusion of gravity. In the weak-gravity limit, the running gauge coupling receives no contribution from the gravitational sector, if all symmetries are preserved. This holds true with and without cosmological constant. We also show that asymptotic freedom persists in general field-theory-based gravity scenarios including gravitational shielding as well as asymptotically safe gravity.     

Solution for static,spherically symmetric Lovelock gravity coupled with Yang–Mills hierarchy

The hierarchies of both Lovelock gravity and power-Yang–Mills field are combined through gravity in a single theory. In static, spherically symmetric ansatz exact particular integrals are obtained in all higher dimensions. The advantage of such hierarchies is the possibility of choosing coefficients, which are arbitrary otherwise, to cast solutions into tractable forms. To our knowledge the solutions constitute the most general spherically symmetric metrics that incorporate complexities both of Lovelock and Yang–Mills hierarchies within the common context. A large portion of our general class of solutions concerns and addresses to black holes for which specific examples are given. Thermodynamical behaviors of the system is briefly discussed in particular dimensions.     

Lie Algebroid Yang–Mills with matter fields

Lie Algebroid Yang–Mills theories are a generalization of Yang–Mills gauge theories, replacing the structural Lie algebra by a Lie Algebroid E$E$. In this note we relax the conditions on the fiber metric of E$E$ for gauge invariance of the action functional. Coupling to scalar fields requires possibly nonlinear representations of Lie Algebroids. In all cases, gauge invariance is seen to lead to a condition of covariant constancy on the respective fiber metric in question with respect to an appropriate Lie Algebroid connection.     

Higher dimensional Yang–Mills black holes in third order Lovelock gravity

By employing the higher (N>5$N>5$)-dimensional version of the Wu–Yang ansatz we obtain magnetically charged new black hole solutions in the Einstein–Yang–Mills–Lovelock (EYML) theory with second (α₂${\alpha }_2$) and third (α₃${\alpha }_3$) order parameters. These parameters, where α₂${\alpha }_2$ is also known as the Gauss–Bonnet parameter, modify the horizons (and the resulting thermodynamical properties) of the black holes. It is shown also that asymptotically (r→∞$r\to \infty$), these parameters contribute to an effective cosmological constant—without cosmological constant—so that the solution behaves de-Sitter (anti de-Sitter) like.     

Einstein–Yang–Mills AdS black brane solution in massive gravity and viscosity bound

We introduce the Einstein–Yang–Mills AdS black brane solution in context of massive gravity. The ratio of shear viscosity to entropy density is calculated for this solution. This value violates the KSS bound if we apply the Dirichlet boundary and regularity on the horizon conditions.     

The one and a half monopoles solution of the SU(2) Yang–Mills–Higgs field theory

Recently we have reported on the existence of finite energy SU(2) Yang–Mills–Higgs particle of one-half topological charge. In this paper, we show that this one-half monopole can co-exist with a ’t Hooft–Polyakov monopole. The magnetic charge of the one-half monopole is of opposite sign to the magnetic charge of the ’t Hooft–Polyakov monopole. However the net magnetic charge of the configuration is zero due to the presence of a semi-infinite Dirac string along the positive z$z$-axis that carries the other half of the magnetic monopole charge. The solution possesses gauge potentials that are singular along the z$z$-axis, elsewhere they are regular. The total energy is found to increase with the strength of the Higgs field self-coupling constant λ$\lambda$. However the dipole separation and the magnetic dipole moment decrease with λ$\lambda$. This solution is non-BPS even in the BPS limit when the Higgs self-coupling constant vanishes.     

Non-Abelian Vortices,Super Yang–Mills Theory and Spin(7)-Instantons

We consider a complex vector bundle E{\mathcal{E}} endowed with a connection A{\mathcal{A}} over the eight-dimensional manifold \mathbbR²×G/H{\mathbb{R}^2\times G/H}, where G/H = SU(3)/U(1) × U(1) is a homogeneous space provided with a never-integrable almost-complex structure and a family of SU(3)-structures. We establish an equivalence between G-invariant solutions A{\mathcal{A}} of the Spin(7)-instanton equations on \mathbbR²×G/H{\mathbb{R}^2\times G/H} and general solutions of non-Abelian coupled vortex equations on \mathbbR²{\mathbb{R}^2}. These vortices are BPS solitons in a d = 4 gauge theory obtained from N = 1{\mathcal{N} =1} supersymmetric Yang–Mills theory in ten dimensions compactified on the coset space G/H with an SU(3)-structure. The novelty of the obtained vortex equations lies in the fact that Higgs fields, defining morphisms of vector bundles over \mathbbR²{\mathbb{R}^2}, are not holomorphic in the generic case. Finally, we introduce BPS vortex equations in N = 4{\mathcal{N} =4} super Yang–Mills theory and show that they have the same feature.     

Quark-confinement mechanism for SU(2) Yang–Mills theory in abelian gauge

By dimensional reduction in the sense of Parisi and Sourlas (PS), the gauge fixing term in the abelian gauge of the SU(2) Yang–Mills field is reduced to a two-dimensional O(3) nonlinear model. The confinement potential is obtained from magnetic monopoles and frame fluctuations. But the source of quark confinement is frame fluctuations and not magnetic monopoles. Because the frame cannot be regarded as a fixed one, the abelian projected SU(2) Yang–Mills field turns into a gauge field – one group element being with fixed frame , another group gauging the frame . The nonperturbative part becomes a dynamical gauge field in two dimensions, giving rise to the short range linear potential. Received: 4 September 2000 / Published online: 23 February 2001     

Hairy Black Hole Solutions¶to SU(3) Einstein–Yang–Mills Equations

We give a rigorous proof of existence of infinitely many black hole solutions to the Einstein–Yang–Mills equations with gauge group SU(3). In the case that the radius of event horizon is not too small, we show that there is a black hole solution for any possible numbers of zeros of the two field variables. Received: 23 October 2000 / Accepted: 30 January 2001     

One-loop photon–photon scattering in a thermal,deconfining SU(2) Yang–Mills plasma

For a deconfining thermal SU(2) Yang–Mills plasma we discuss the role of (anti)calorons in introducing non-thermal behavior effectively described in terms of Planck’s quantum of action ?$?$. This non-thermality cancels exactly between the ground-state estimate and its free quasiparticle excitations. Kinematic constraints in 4-vertex scattering and the counting of radial loop variables versus the number of independent constraints on them are re-visited. Next, we consider thermal 2→2$2\to 2$ one-loop scattering of the modes remaining massless upon the (anti)caloron induced adjoint Higgs mechanism (thermal ground state after spatial coarse graining). Starting with stringent analytical arguments, we are able to exclude the contribution to photon–photon scattering from diagrams containing at least one three-vertex and, in a next step, a vast majority of all possible configurations involving two four-vertices. By numerical analysis we show that the remaining contribution of the overall S channel is severely suppressed compared those of the T and U channels, meaning that the creation of a pair of massive vector modes by a pair of photons and vice versa practically does not occur in the Yang–Mills plasma. For the T and U channels the domain of loop integration represents less than 10⁻⁷$10^{-7}$ times the volume of the unconstrained integration region. The thus introduced photon–photon correlation should affect the Cosmic Microwave Background’s polarization at low redshift. An adaption of the here-developed methods to the analysis of irreducible bubble diagrams could prove the conjecture of hep-th/0609033 on the termination of the loop expansion of thermodynamical quantities at a finite irreducible order.     

Center vortex properties in the Laplace-center gauge of SU(2) Yang–Mills theory

Resorting to the the Laplace center gauge (LCG) and to the Maximal-center gauge (MCG), respectively, confining vortices are defined by center projection in either case. Vortex properties are investigated in the continuum limit of SU(2) lattice gauge theory. The vortex (area) density and the density of vortex crossing points are investigated. In the case of MCG, both densities are physical quantities in the continuum limit. By contrast, in the LCG the piercing as well as the crossing points lie dense in the continuum limit. In both cases, an approximate treatment by means of a weakly interacting vortex gas is not appropriate.     

New Types of Solutions for the Classic 3D SU (2) Yang–Mills Equations

Doklady Physics - New types of 3D solutions for the classic Yang–Mills equations in the Faddeev–Niemi reformulation are found. In a particular case, these solutions describe 3D vortices.     

A Semi-Analytical Solution to Classic Yang–Mills Equations with Both Asymptotical Freedom and Confining Features

It is well known that confinings and asymptotic freedom are properties of quantum chromo-dynamics(QCD).But hints of these features can also be observed at purely classic levels.For this purpose we need to find solutions to the colorly-sourceful Yang–Mills equations with both confining and asymptotic freedom features.We provide such a solution in this paper which at the near-source region is of serial form,while at the far-away region is approximately expressed through simple elementary functions.From the solution,we derive out a classically non-perturbative beta function describing the running of efective coupling constant,which is linear in the couplings both in the infrared and ultraviolet region.     

Some solutions of the Gauss–Bonnet gravity with scalar field in four dimensions

We give all exact solutions of the Einstein–Gauss–Bonnet Field Equations coupled with a scalar field in four dimensions under certain assumptions. The main assumption we make in this work is to take the second covariant derivative of the coupling function proportional to the spacetime metric tensor. Although this assumption simplifies the field equations considerably, to obtain exact solutions we assume also that the spacetime metric is conformally flat. Then we obtain a class of exact solutions.