Slavnov–Taylor identities in Coulomb gauge Yang–Mills theory

The Slavnov–Taylor identities of Coulomb gauge Yang–Mills theory are derived from the (standard, second order) functional formalism. It is shown how these identities form closed sets from which one can in principle fully determine the Green’s functions involving the temporal component of the gauge field without approximation, given appropriate input.     

Equal-time two-point correlation functions in Coulomb gauge Yang–Mills theory

We apply a functional perturbative approach to the calculation of the equal-time two-point correlation functions and the potential between static color charges to one-loop order in Coulomb gauge Yang–Mills theory. The functional approach proceeds through a solution of the Schrödinger equation for the vacuum wave functional to order g²$g^2$ and derives the equal-time correlation functions from a functional integral representation via new diagrammatic rules. We show that the results coincide with those obtained from the usual Lagrangian functional integral approach, extract the beta function, and determine the anomalous dimensions of the equal-time gluon and ghost two-point functions and the static potential under the assumption of multiplicative renormalizability to all orders.     

The exact decomposition of gauge variables in lattice Yang–Mills theory

In this Letter, we consider lattice versions of the decomposition of the Yang–Mills field a la Cho–Faddeev–Niemi, which was extended by Kondo, Shinohara and Murakami in the continuum formulation. For the SU(N)$\mathit{SU}(N)$ gauge group, we propose a set of defining equations for specifying the decomposition of the gauge link variable and solve them exactly without using the ansatz adopted in the previous studies for SU(2)$\mathit{SU}(2)$ and SU(3)$\mathit{SU}(3)$. As a result, we obtain the general form of the decomposition for SU(N)$\mathit{SU}(N)$ gauge link variables and confirm the previous results obtained for SU(2)$\mathit{SU}(2)$ and SU(3)$\mathit{SU}(3)$.     

Yang–Mills on Quantum Heisenberg Manifolds

In the noncommutative geometry program of Connes, there are two variations of the concept of the Yang–Mills action functional. We show that for the quantum Heisenberg manifolds for generic parameter values they agree.     

Mathematical quantum Yang–Mills theory revisited

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 nonperturbative, without cut-offs, and agrees with the causality and stability principles. This paper presents a fully revised, simplified, and corrected version of the corresponding material in the previous papers Dynin ([11] and [12]). The principal result is established anew: due to the quartic self-interaction term in the Yang–Mills Lagrangian along with the semisimplicity of the gauge group, the quantum Yang–Mills energy spectrum has a positive mass gap. Furthermore, the quantum Yang–Mills Hamiltonian has a countable orthogonal eigenbasis in a Fock space, so that the quantum Yang–Mills spectrum is point and countable. In addition, a fine structure of the spectrum is elucidated.     

Towards a Loop Quantum Gravity and Yang–Mills unification

We propose a new method of unifying gravity and the Standard Model by introducing a spin-foam model. We realize a unification between an SU(2)$\mathit{SU}(2)$ Yang–Mills interaction and 3D   general relativity by considering a constrained Spin(4)∼SO(4)$\mathrm{Spin}(4)\sim \mathit{SO}(4)$ Plebanski action. The theory is quantized à la   spin-foam by implementing the analogue of the simplicial constraints for the Spin(4)$\mathrm{Spin}(4)$ symmetry, providing a way to couple Yang–Mills fields to spin-foams. A natural 4D extension of the theory is introduced. We also present a way to recover 2-point correlation functions between the connections as a first way to implement scattering amplitudes between particle states, aiming to connect Loop Quantum Gravity to new physical predictions.     

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     

Confinement in a three-dimensional Yang–Mills theory

We show that, starting from known exact classical solutions of the Yang–Mills theory in three dimensions, the string tension is obtained and the potential is consistent with a marginally confining theory. The potential we obtain agrees fairly well with preceding findings in the literature but here we derive it analytically from the theory without further assumptions. The string tension is in strict agreement with lattice results and the well-known theoretical result by Karabali–Kim–Nair analysis. Classical solutions depend on a dimensionless numerical factor arising from integration. This factor enters into the determination of the spectrum and has been arbitrarily introduced in some theoretical models. We derive it directly from the solutions of the theory and is now fully justified. The agreement obtained with the lattice results for the ground state of the theory is well below 1% at any value of the degree of the group.     

Super Yang–Mills theory from nonlinear supersymmetry

The relation between a nonlinear supersymmetric (NLSUSY) theory and a SUSY Yang–Mills (SYM) theory is studied for N=3$N=3$ SUSY in two-dimensional space–time. We explicitly show the NL/L SUSY relation for the (pure) SYM theory by means of cancellations among Nambu–Goldstone fermion self-interaction terms.     

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.     

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.     

The Boltzmann equation in classical Yang–Mills theory

We give a detailed derivation of the Boltzmann equation, and in particular its collision integral, in classical field theory. We first carry this out in a scalar theory with both cubic and quartic interactions and subsequently in a Yang–Mills theory. Our method does not rely on a doubling of the fields, rather it is based on a diagrammatic approach representing the classical solution to the problem.     

Yang–Mills Algebra

Some unexpected properties of the cubic algebra generated by the covariant derivatives of a generic Yang–Mills connection over the (s+1)-dimensional pseudo Euclidean space are pointed out. This algebra is Koszul of global dimension 3 and Gorenstein but except for s=1 (i.e. in the two-dimensional case) where it is the universal enveloping algebra of the Heisenberg Lie algebra and is a cubic Artin–Schelter regular algebra, it fails to be regular in that it has exponential growth. We give an explicit formula for the Poincaré series of this algebra and for the dimension in degree n of the graded Lie algebra of which is the universal enveloping algebra. In the four-dimensional (i.e. s=3) Euclidean case, a quotient of this algebra is the quadratic algebra generated by the covariant derivatives of a generic (anti) self-dual connection. This latter algebra is Koszul of global dimension 2 but is not Gorenstein and has exponential growth. It is the universal enveloping algebra of the graded Lie algebra which is the semi-direct product of the free Lie algebra with three generators of degree one by a derivation of degree one.     

Four-dimensional Yang–Mills theory with a three-dimensional fermion membrane

We study the four-dimensional Yang–Mills theory in the presence of a three-dimensional membrane of fermions by lattice Monte Carlo simulations. We analyze the phase structure of this theory at finite temperature. Below the phase transition temperature of the pure Yang–Mills theory, we obtain an unconventional phase with spatially-nonuniform vacuum. In this phase, the expectation value of the Polyakov loop is finite on the membrane, and it exponentially decays to zero outside the membrane.     

Homological perspective on edge modes in linear Yang–Mills and Chern–Simons theory

Letters in Mathematical Physics - We provide an elegant homological construction of the extended phase space for linear Yang–Mills theory on an oriented and time-oriented Lorentzian manifold...     

Renormalization aspects of \mathcal {N}=1 Super Yang–Mills theory in the Wess–Zumino gauge

The generalized $f(R)$ gravity with curvature–matter coupling in five-dimensional (5D) spacetime can be established by assuming a hypersurface-orthogonal space-like Killing vector field of 5D spacetime, and it can be reduced to the 4D formalism of FRW universe. This theory is quite general and can give the corresponding results for Einstein gravity, and $f(R)$ gravity with both no-coupling and non-minimal coupling in 5D spacetime as special cases, that is, we would give some new results besides previous ones given by Huang et al. in Phys Rev D 81:064003, 2010. Furthermore, in order to get some insight into the effects of this theory on the 4D spacetime, by considering a specific type of models with $f_{1}(R)=f_{2}(R)=\alpha R^{m}$ and $B(L_{m})=L_{m}=-\rho $ , we not only discuss the constraints on the model parameters $m,n$ , but also illustrate the evolutionary trajectories of the scale factor $a(t)$ , the deceleration parameter $q(t)$ , and the scalar field $\epsilon (t),\phi (t)$ in the reduced 4D spacetime. The research results show that this type of $f(R)$ gravity models given by us could explain the current accelerated expansion of our universe without introducing dark energy.