Presence Of Gauge Field Research Articles

Stochastic field theory for a dirac particle propagating in gauge field disorder

Recent theoretical and numerical developments show analogies between quantum chromodynamics (QCD) and disordered systems in condensed matter physics. We study the spectral fluctuations of a Dirac particle propagating in a finite four-dimensional box in the presence of gauge fields. We construct a model which combines Efetov's approach to disordered systems with the principles of chiral symmetry and QCD. To this end, the gauge fields are replaced with a stochastic white-noise potential, the gauge field disorder. Effective supersymmetric nonlinear sigma models are obtained. Spontaneous breaking of supersymmetry is found. We rigorously derive the equivalent of the Thouless energy within our generic model implying the universality of this scale in QCD. Connections to other low energy effective theories, in particular, the Nambu-Jona-Lasinio model and chiral perturbation theory, are found.

Effective description of axion defects

Axion strings and domain walls exhibit a number of novel effects in the presence of gauge fields, in particular the electromagnetic field. It is shown how these effects are reproduced in a model of Nambu-Goto-type strings and open or closed membranes coupled to gauge fields. The generalization to “axionic p-branes” is considered and it is shown how worldvolume gauge fields that arise in certain cases can be interpreted as Goldstone fields.

NEURAL MULTIGRID METHODS FOR GAUGE THEORIES AND OTHER DISORDERED SYSTEMS

We present evidence that multigrid works for wave equations in disordered systems, e.g. in the presence of gauge fields, no matter how strong the disorder, but one needs to introduce a "neural computations" point of view into large scale simulations: First, the system must learn how to do the simulations efficiently, then do the simulation (fast). The method can also be used to provide smooth interpolation kernels which are needed in multigrid Monte Carlo updates.

The dynamics of a flat Friedmann-Robertson-Walker inflationary model in the presence of gauge fields

The authors study the dynamics of a flat Friedmann-Robertson-Walker (FRW) inflationary model in the presence of gauge fields. A qualitative analysis of the dynamical system associated with their model is presented. It is shown that inflation is a general property and that the gauge field enhances inflation.

Multigrid meets neural nets

We present evidence that multigrid (MG) works for wave equations in disorded systems, e.g. in the presence of gauge fields, no matter how strong the disorder. We introduce a “neural computations” point of view into large scale simulations: First, the system must learn how to do the simulations efficiently, then do the simulation (fast). The method can also be used to provide smooth interpolation kernels which are needed in multigrid Monte Carlo updates.

Projective multigrid method for propagators in lattice gauge theory.

A projective multigrid method is considered for application to fermion propagators in the presence of gauge fields. The collective variables on each block are defined by the gauge-invariant projection onto the lowest eigenstate for the block. The scheme is formulated in detail for twodimensional bosons and Wilson fermions in the U(1) gauge theory and numerical studies are presented for bosons to demonstrate its potential for more efficient convergence. For example, at a confinement length of 8 lattice units on a 64\ifmmode\times\else\texttimes\fi{}64 lattice, the projective multigrid method gives a speed up of almost two orders of magnitude relative to the Gauss-Seidel algorithm.

Supersymmetric vacuum alignment, chiral fermions, quark-lepton universality and MW/(MZ cos θW)

Implicit global symmetries of the standard model, such as the SU(4) underlying quark-lepton universality or the custodial SU(2) responsible for rho =MW/MZ cos theta W=1, as well as the chiral spectrum of quarks and leptons, can be explained by the dynamics of vacuum alignment in supersymmetric composite models. The general theory of supersymmetric vacuum alignment is summarised and a simple formula is derived which determines the alignment in the presence of gauge fields, including a Fayet-Iliopoulos U(1) (1974). In the one-generation preon model of Barbieri, Masiero and Veneziano (1983), this resolution of the vacuum alignment problem requires the enlargement of the standard model gauge group to include chiral colour and extra U(1) factors. These extra gauge groups are all spontaneously broken, leaving a light fermion spectrum comprising only quarks, leptons and leptoquarks.

A systematic study of the low energy effects of heavy particles in the standard model

In this approach, at any loop order, the low energy effects of a heavy Higgs boson and a heavy fermion can be summarized by an effective lagrangian. To the one-loop order, an effective lagrangian for the bosonic sector of the theory is constructed. One fermion mass is light ( m) and the other is heavy ( M). At the one-loop level heavy fermion mass effects proportional to M 2and ln( M/ m) have been found. It is shown here that in the presence of gauge fields, the infinites 1/ϵ of the nonlinear σ-model do not fully reproduce the ln( M H) of the linear σ-model.

Non-abelian bosonization in two dimensions using path integrals

We use path integral methods to convert a non-abelian theory of fermions interacting with gauge fields (QCD 2) in (1 + 1) dimensions into an equivalent bose theory. While our results reduce to those obtained by Witten for the special case of a free theory, we show that his bose-fermi operator identification must be modified in the presence of gauge fields. Our methods also reveal potential difficulties in using this operator equivalence even for the free theory. We also introduce the concept of limited bosonization-using a bose theory to reproduce only some of the fermion Green functions-and discuss its consequences.

On the influence of extra dimensions on the homogeneous isotropic universe

The model of a homogeneous isotropic universe is studied in the presence of gauge fields, noninteracting dust, and two extra compact dimensions. It is found that the singular “big bang” type solution can be rejected because of the drastic growth of the radius of the universe. On the other hand, solutions without singularity can be found showing a very rapid oscillation (Planck frequency) with small amplitude around the data prescribing the present status of the universe.