Vacuum Field Configurations Research Articles

On microscopic structure of the QCD vacuum

We propose a new class of regular stationary axially symmetric solutions in a pure QCD which correspond to monopole–antimonopole pairs at macroscopic scale. The solutions represent vacuum field configurations which are locally stable against quantum gluon fluctuations in any small space–time vicinity. This implies that the monopole–antimonopole pair can serve as a structural element in microscopic description of QCD vacuum formation.

More on two-dimensionalO(N)models withN=(0,1)supersymmetry

We study the behavior of two dimensional supersymmetric connections of $n$ copies of $O(N)$ models with an $\mathcal{N} = (0,1)$ heterotic deformation generated by a right moving fermion. We develop the model in analogy with the connected $\mathcal{N}=(0,2)$ $CP(N-1)$ models for the case of a single connecting fermionic superfield. We calculate the effective potential in the large $N$ limit and determine the vacuum field configurations. Similarily to other SUSY connected models we find that SUSY is unbroken under certain conditions despite the vanishing of the Witten index. Specifically, this preservation of SUSY occurs when we have an even number $n$ of $O(N)$ families. As in previous cases we show that this result follows from a $Z_n$ symmetry under a particular exchange of the $O(N)$ families. This leads to a definition of a modified Witten index, which gaurantees the preservation of SUSY in this case.

The role of magnetic field in the transition to streaming ablation in wire arrays

In wire array Z-pinches, the magnetic field configuration and the global field penetration of individual wires play a key role in the ablation plasma dynamics. Knowledge of the magnetic field configuration is necessary to understand the ablation plasma acceleration process near the wires. Two-dimensional resistive magnetohydrodynamics simulations show that a change in the global magnetic field configuration is critical to initiating inward flow of the ablation plasma. Analysis of these simulations show that the initially compressive J×B force around a wire in its vacuum field configuration undergoes a transition to a configuration in which the Lorentz force can accelerate plasma toward the array axis. This transition is achieved through a low magnetic Reynolds number diffusive flow in which the plasma and the magnetic field are decoupled. The plasma current follows the expanding plasma toward the array axis and, after traveling a critical distance scaling with the array radius divided by the wire number, the global magnetic field threads the wire core, thereby allowing J×B coronal acceleration into ablation streams.

Quantum interactions between nonperturbative vacuum fields

We develop an approach to investigate the non-perturbative dynamics of quantum field theories, in which specific vacuum field fluctuations are treated as the low-energy dynamical degrees of freedom, while all other vacuum field configurations are explicitly integrated out from the path integral. We show how to compute the effective interaction between the vacuum field degrees of freedom both perturbatively (using stochastic perturbation theory) and fully non-perturbatively (using lattice field theory simulations). The present approach holds to all orders in the couplings and does not rely on the semi-classical approximation.

On vacuum structures of [formula omitted] LSUSY QED equivalent to [formula omitted] NLSUSY model

The vacuum structure of N=2 linear supersymmetry (LSUSY) invariant QED, which is equivalent to N=2 nonlinear supersymmetry (NLSUSY) model, is studied explicitly in two-dimensional space–time (d=2). Two different isometries SO(1,3) and SO(3,1) appear for the vacuum field configuration corresponding to the various parameter regions. Two different field configurations of SO(3,1) isometry describe the two different physical vacua, i.e. one breaks spontaneously both U(1) and SUSY and the other breaks spontaneously SUSY alone.

Global three-dimensional calculations of ion-temperature-gradient modes in stellarators with a two-fluid model

Ion-temperature-gradient (ITG) driven modes in general three-dimensional geometry are investigated using a physical model based on the linearized Braginskii two-fluid equations. The resulting equations are solved globally as an eigenvalue problem without using the ballooning approximation. As a first application of the code developed we calculate the most unstable ITG modes for vacuum field configurations of an ℓ = 2 stellarator and the Wendelstein 7-X (W7-X) stellarator.The Fourier spectra of the modes found do not show a pronounced influence of three-dimensional geometry. The space structure of the solution for the ℓ = 2 stellarator configuration is nearly axisymmetric, while for the W7-X configuration it is more complicated. The properties of the solutions are discussed in connection with the two-fluid model used.

Warped, anisotropic wormhole/soliton configurations in vacuum 5D gravity

In this paper we apply the anholonomic frames method developed in previous work to construct and study anisotropic vacuum field configurations in 5D gravity. Starting with an off-diagonal 5D metric, parametrized in terms of several ansatz functions, we show that using anholonomic frames greatly simplifies the resulting Einstein field equations. These simplified equations contain an interesting freedom in that one can choose one of the ansatz functions and then determine the remaining ansatz functions in terms of this choice. As examples we take one of the ansatz functions to be a solitonic solution of either the Kadomtsev–Petviashvili equation or the sine-Gordon equation. There are several interesting physical consequences of these solutions. First, a certain subclass of the solutions discussed in this paper has an exponential warp factor similar to that of the Randall–Sundrum model. However, the warp factor depends on more than just the fifth coordinate. In addition the warp factor arises from anisotropic vacuum solutions rather than from any explicit matter. Second, the solitonic character of these solutions might allow them to be interpreted either as gravitational models for particles (i.e. analogous to the 't Hooft–Polyakov monopole, but in the context of gravity), or as nonlinear, anisotropic gravitational waves.

Monopoles and hybrids in Abelian projection of lattice QCD

We study topological defects constructed from diagonal and non-diagonal gluons in Abelian projection of zero temperature lattice QCD. We compare results obtained in the quenched and non-quenched vacuum field configurations and show that the density of hybrids is higher than the density of monopoles. The density of some hybrids is sensitive to the presence of the virtual fermions.

Finding topological solitary waves in models with non-equivalent vacua

We study the existence of bidimensional bosonic models for which the spontaneous symmetry breaking phenomenon yields, at classical level, non-equivalent vacua. Once we introduce the concept of vacuum manifold V , defined in terms of the vacuum field configurations, the behavior of the models at issue can be analyzed by means of the so-called classical moduli space M c ( V) . The aforementioned structure allows us to classify the kink-like excitations into loops and links. To be precise, the loops interpolate smoothly between equivalent minima of the classical potential while the links connect vacua located at different points in M c ( V) . Although exact results are very hard to come by, we resort to models simple enough to provide us with the solitary waves in closed form.

Bidimensional Supersymmetric Field Theories with Discrete Moduli Space

We consider bidimensional supersymmetric models for which the classical theory has a discrete set of inequivalent vacua. Once we introduce the concept ofvacuum manifoldV, defined in terms of all the vacuum field configurations, the properties of such models can be described by means of theclassical moduli spaceMc(V). Quantum corrections, perturbative and nonperturbative, do not lift the vacuum degeneracy so that the quantum theory as a whole exhibits non-trivialquantum moduli spaceMq(V). The former structure allows us to classify the kink-like excitations intoloopsandlinks:loopsinterpolate smoothly between equivalent vacua whilelinksconnect vacua located at different points in Mq(V).

Microcavity vacuum-field configuration and the spontaneous emission power

The axial and lateral spontaneous emission intensities from vertical-cavity laser diodes have been studied both experimentally and theoretically. The measurements show that spontaneous emission from the cavity perimeter (lateral emission) is overwhelmingly larger than the same emanating along the lasing direction (axial emission). A model for lateral and axial spontaneous emission from microcavities is postulated based on one- and two-dimensional vacuum electromagnetic field confinement, respectively. A new cavity mode counting technique is developed and utilized to calculate the spontaneous emission initio. The resulting field configuration theory is in good agreement with the emission intensity measurements. >

Cosmological sphaleron from real tunneling and its fate.

We show that the cosmological sphaleron of the Einstein-Yang-Mills system can be produced from real tunneling geometries. The sphaleron will tend to roll down to the vacuum or pure gauge field configuration, when the universe evolves in the Lorentzian signature region with the sphaleron and the corresponding hypersurface being the initial data for the Yang-Mills field and the universe, respectively. However, we can also show that the sphaleron, although unstable, can be regarded as a pseudostable solution because its lifetime is even much greater than that of the universe.

THE SPINNING MEMBRANE, SUPER-SU(∞)-GAUGE THEORIES AND MOYAL BRACKETS

Several important topics concerning the membrane and its symmetries are discussed. The fact that a space–time-independent Lagrangian density for a gauge-field configuration of a (d – 1)-dimensional SU (∞) super Yang–Mills theory, reduced to one dimension (time), is equivalent to a Green–Schwarz formalism of the Euclidean Eguchi–Schild string action in d – 1 dimensions, naturally raises the question whether one can construct a Neveu–Ramond–Schwarz analog. The answer is in the negative; the world-sheet supersymmetric extension of the Eguchi–Schild action for the string cannot be viewed as a classical-vacuum configuration of a super-SU (∞)- gauge theory. For the second topic we construct a "supersymmetry" charge operator, Qf, which plays the role of a residual fermionic symmetry, for fixed time, of the light-cone spinning membrane. It is explicitly shown how the Yang–Mills type of actions and, in particular, the ones for vacuum-field configurations, associated with Q(∞) supergauge theories, are invariant under both Qf "supersymmetry" and the superalgebra of area-preserving superdiffeomorphisms of the light-cone spinning torus membrane, Q(∞). More general actions can be constructed which are invariant under deformations of this superalgebra. In this case the ordinary (graded) Poisson brackets are replaced by super Moyal brackets. Finally, we conjecture why these actions, in analogy with what happens with the light-cone supermembrane, should correspond to a superfiber bundle (over space–time) formulation of the supersymmetric-gauge quantum-mechanical models (SGQMM's) of Flume and Baake et al.; with the general supergroup of trigonometric structure constants of Fairlie, Fletcher and Zachos as the structure supergroup of the superfiber. To support our concluding conjecture, preliminary steps are outlined which are necessary in order to fix the light-cone gauge for the spinning-membrane action. We discuss why the Qf "supersymmetry" (the remnant world-volume light-cone local supersymmetry) and the Q(∞) supergauge transformations must arise as its residual symmetries.

Effect of Vacuum Magnetic Well on Magnetohydrodynamic Stability in Heliotron-E-like Configurations with High Shear

An analysis of n ≥ 1 free-boundary modes in Heliotron-E-like configurations using the stellarator expansion code STEP is given. It is shown that an axisymmetric quadrupol field improves the stability properties of these high-shear equilibria. The corresponding vacuum quadrupole field is used to find vacuum field configurations with an average magnetic well of (ΔV' / V')min = -4 % .

Dynamically selected vacuum field configuration in massless QED.

Using the Euclidean functional-integral formalism an effective bilocal action is derived for massless quantum electrodynamics (QED). The vacuum field equation is obtained from this action and it is shown that the dynamically selected vacuum field configuration in massless QED is a class of degenerate, nontrivial field configurations related to each other through a one-parameter Abelian chiral transformation. The existence of a chirally degenerate vacuum establishes that the chiral symmetry manifest in the action of massless QED becomes a hidden symmetry when a particular choice of the vacuum configuration is made. Thus it is established that chiral symmetry is spontaneously broken in the vacuum of massless QED.

Use of the stellarator expansion to investigate plasma equilibrium in stellarators

A numerical code utilizing a large-aspect-ratio, small -helical-distortion expansion is developed and used to investigate the effect of plasma currents on stellarator equilibrium. Application is made to several existing and proposed stellarators. The modification of the equilibrium properties with pressure is strongly dependent on the vacuum-field configuration. The modular stellarator model which is investigated gives somewhat discouraging results because a large rotational transform, and hence large coil deformation, is needed to achieve high-beta equilibria.

Theoretical Optimization of Stellarators

Net current free toroidal (stellarator) confinement is studied with a combination of several methods: a complete set of analytical vacuum fields for finding favorable vacuum field configurations; three-dimensional MHD codes for finite-s, equilibrium computations; the expansion of a general toroidal equilibrium around its magnetic axis as guideline for the computational search in configurational space and for finite-s, MHD stability; Monte Carlo simulations for particle containment; continuous modular coil systems generating the configurations considered. Results are: vacuum field configurations with sizeable Q = 0, 1, 2, 3 helical fields, substantial twist number (? 1/2), significant reduction of the parallel current density, and vacuum magnetic well exist for a toroidal aspect ratio of 15-20 and can be generated by modular coils whose excursions from meridional planes are small compared to the toroidal period length. In these configurations, the finite-s toroidal shift is strongly reduced, so that a larger s value (factor 2-4) than in the equivalent Q = 2 stellarator can be achieved. Stability calculations do not exclude the possibility of stable equilibria of this kind with (s) ? 0.05-0.1; transport calculations without electrical field show improvement-as compared to the Q = 2 stellarator-in the collisional and plateau regimes.

Structure of the gauge theory vacuum at finite temperatures

The space of moduli, i.e., the space of field configurations modulo gauge equivalence is constructed for calorons (self-dual gauge fields on R/sup 3/ x S/sup 1/) with vanishing topological charge. Such calorons represent vacuum field configurations at a finite temperature. It is found that, unlike its zero-temperature counterpart, this space of moduli is nontrivial, being, in fact, a one-dimensional manifold.

Quantum decay process of metastable vacuum states in SU(2) Yang-Mills theory: A probability theoretical point of view

The problem of vacuum-tunneling phenomena such as the quantum decay process of metastable vacuum states in SU(2) Yang-Mills theory is investigated from a probability theoretical point of view. This is done by adopting the stochastic quantization procedure to quantize the Yang-Mills field in the A/sub 0/ = 0 gauge. The mechanism of vacuum tunneling can be illustrated within the realm of the stochastic quantization. It is shown that the quantized vacuum field configuration, which manifests the decay process of metastable vacuum states, is a Euclidean-Markov field of Gaussian type. The validity of the Euclidean path-integral description of vacuum-tunneling phenomena is also shown from the probability theoretical point of view. Passing to the semiclassical limit, the concept of an instanton is justified as a classical Euclidean Yang-Mills field which manifests the most probable tunneling path.

Existence of Mirror Machines Stable Against Interchange Modes

The existence of a wide class of poloidal vacuum-field configurations where the magnetic field has a finite local minimum value on a circle is pointed out, and this phenomena is related to the existence of stable mirror machines. (C.E.S.)