Fixed Point Action and Topology in the CP^3 Model

We define a fixed point action in two-dimensional lattice ${\rm CP}^{N-1}$ models. The fixed point action is a classical perfect lattice action, which is expected to show strongly reduced cutoff effects in numerical simulations. Furthermore, the action has scale-invariant instanton solutions, which enables us to define a correct topological charge without topological defects. Using a parametrization of the fixed point action for the ${\rm CP}^{3}$ model in a Monte Carlo simulation, we study the topological susceptibility.Comment: 27 pages, 5 figures, typeset using REVTEX, Sec. 6 rewritten (additional numerical results), to be published in Phys.Rev.

Topological Lattice Actions

We consider lattice field theories with topological actions, which are invariant against small deformations of the fields. Some of these actions have infinite barriers separating different topological sectors. Topological actions do not have the correct classical continuum limit and they cannot be treated using perturbation theory, but they still yield the correct quantum continuum limit. To show this, we present analytic studies of the 1-d O(2) and O(3) model, as well as Monte Carlo simulations of the 2-d O(3) model using topological lattice actions. Some topological actions obey and others violate a lattice Schwarz inequality between the action and the topological charge Q. Irrespective of this, in the 2-d O(3) model the topological susceptibility \chi_t = \l/V is logarithmically divergent in the continuum limit. Still, at non-zero distance the correlator of the topological charge density has a finite continuum limit which is consistent with analytic predictions. Our study shows explicitly that some classically important features of an action are irrelevant for reaching the correct quantum continuum limit.Comment: 38 pages, 12 figure

Quenched divergences in the deconfined phase of SU(2) gauge theory

The spectrum of the overlap Dirac operator in the deconfined phase of quenched gauge theory is known to have three parts: exact zeros arising from topology, small nonzero eigenvalues that result in a non-zero chiral condensate, and the dense bulk of the spectrum, which is separated from the small eigenvalues by a gap. In this paper, we focus on the small nonzero eigenvalues in an SU(2) gauge field background at $\beta=2.4$ and $N_T=4$. This low-lying spectrum is computed on four different spatial lattices ($12^3$, $14^3$, $16^3$, and $18^3$). As the volume increases, the small eigenvalues become increasingly concentrated near zero in such a way as to strongly suggest that the infinite volume condensate diverges.Comment: 12 pages, 3 figures, version to appear in Physical Review

Boundary Limitation of Wavenumbers in Taylor-Vortex Flow

We report experimental results for a boundary-mediated wavenumber-adjustment mechanism and for a boundary-limited wavenumber-band of Taylor-vortex flow (TVF). The system consists of fluid contained between two concentric cylinders with the inner one rotating at an angular frequency $\Omega$. As observed previously, the Eckhaus instability (a bulk instability) is observed and limits the stable wavenumber band when the system is terminated axially by two rigid, non-rotating plates. The band width is then of order $\epsilon^{1/2}$ at small $\epsilon$ ($\epsilon \equiv \Omega/\Omega_c - 1$) and agrees well with calculations based on the equations of motion over a wide $\epsilon$-range. When the cylinder axis is vertical and the upper liquid surface is free (i.e. an air-liquid interface), vortices can be generated or expelled at the free surface because there the phase of the structure is only weakly pinned. The band of wavenumbers over which Taylor-vortex flow exists is then more narrow than the stable band limited by the Eckhaus instability. At small $\epsilon$ the boundary-mediated band-width is linear in $\epsilon$. These results are qualitatively consistent with theoretical predictions, but to our knowledge a quantitative calculation for TVF with a free surface does not exist.Comment: 8 pages incl. 9 eps figures bitmap version of Fig

Eigenvalues of the hermitian Wilson-Dirac operator and chiral properties of the domain-wall fermion

Chiral properties of QCD formulated with the domain-wall fermion (DWQCD) are studied using the anomalous quark mass m_{5q} and the spectrum of the 4-dimensional Wilson-Dirac operator. Numerical simulations are made with the standard plaquette gauge action and a renormalization-group improved gauge action. Results are reported on the density of zero eigenvalue obtained with the accumulation method, and a comparison is made with the results for m_{5q}.Comment: Lattice 2000(Chiral Fermions), 4 pages, 6 eps figures, LaTeX(espcrc2.sty

Light Hadron Spectrum and Quark Masses from Quenched Lattice QCD

We present details of simulations for the light hadron spectrum in quenched QCD carried out on the CP-PACS parallel computer. Simulations are made with the Wilson quark action and the plaquette gauge action on 32^3x56 - 64^3x112 lattices at four lattice spacings (a \approx 0.1-0.05 fm) and the spatial extent of 3 fm. Hadronic observables are calculated at five quark masses (m_{PS}/m_V \approx 0.75 - 0.4), assuming the u and d quarks being degenerate but treating the s quark separately. We find that the presence of quenched chiral singularities is supported from an analysis of the pseudoscalar meson data. We take m_\pi, m_\rho and m_K (or m_\phi) as input. After chiral and continuum extrapolations, the agreement of the calculated mass spectrum with experiment is at a 10% level. In comparison with the statistical accuracy of 1-3% and systematic errors of at most 1.7% we have achieved, this demonstrates a failure of the quenched approximation for the hadron spectrum: the meson hyperfine splitting is too small, and the octet masses and the decuplet mass splittings are both smaller than experiment. Light quark masses are calculated using two definitions: the conventional one and the one based on the axial-vector Ward identity. The two results converge toward the continuum limit, yielding m_{ud}=4.29(14)^{+0.51}_{-0.79} MeV. The s quark mass depends on the strange hadron mass chosen for input: m_s = 113.8(2.3)^{+5.8}_{-2.9} MeV from m_K and m_s = 142.3(5.8)^{+22.0}_{-0} MeV from m_\phi, indicating again a failure of the quenched approximation. We obtain \Lambda_{\bar{MS}}^{(0)}= 219.5(5.4) MeV. An O(10%) deviation from experiment is observed in the pseudoscalar meson decay constants.Comment: 60 pages, 49 figure

Quenched QCD with O(a) improvement: I. The spectrum of light hadrons

We present a comprehensive study of the masses of pseudoscalar and vector mesons, as well as octet and decuplet baryons computed in O(a) improved quenched lattice QCD. Results have been obtained using the non-perturbative definition of the improvement coefficient c_sw, and also its estimate in tadpole improved perturbation theory. We investigate effects of improvement on the incidence of exceptional configurations, mass splittings and the parameter J. By combining the results obtained using non-perturbative and tadpole improvement in a simultaneous continuum extrapolation we can compare our spectral data to experiment. We confirm earlier findings by the CP-PACS Collaboration that the quenched light hadron spectrum agrees with experiment at the 10% level.Comment: 36 pages, 7 postscript figures, REVTEX; typo in Table XVIII corrected; extended discussion of finite-size effects in sections III and VII; version to appear in Phys. Rev.

Grand Unification Scale CP Violating Phases And The Electric Dipole Moment

The question of CP violating phases in supersymmetry and electric dipole moments (EDMs) is considered within the framework of supergravity grand unification (GUT) models with a light ($\stackrel{<}{\sim}$1 TeV) mass spectrum. In the minimal model, the nearness of the t-quark Landau pole automatically suppresses the t-quark cubic soft breaking phase at the electroweak scale. However, current EDM data require the quadratic soft breaking phase to be small at the electroweak scale unless tan$\beta$ is small (tan$\beta\stackrel{<}{\sim}$3), and the EDM data combined with the requirement of electroweak symmetry breaking require this phase to be both large and highly fine tuned at the GUT scale unless tan$\beta$ is small. Non minimal models are also examined, and generally show the same behavior.Comment: 28 pages, latex, 15 figure

Phase structure and critical temperature of two-flavor QCD with a renormalization group improved gauge action and clover improved Wilson quark action

We study the finite-temperature phase structure and the transition temperature of QCD with two flavors of dynamical quarks on a lattice with the temporal size $N_t=4$, using a renormalization group improved gauge action and the Wilson quark action improved by the clover term. The region of a parity-broken phase is identified, and the finite-temperature transition line is located on a two-dimensional parameter space of the coupling ($\beta=6/g^2$) and hopping parameter $K$. Near the chiral transition point, defined as the crossing point of the critical line of the vanishing pion mass and the line of finite-temperature transition, the system exhibits behavior well described by the scaling exponents of the three-dimensional O(4) spin model. This indicates a second-order chiral transition in the continuum limit. The transition temperature in the chiral limit is estimated to be $T_c = 171(4)$ MeV.Comment: Typographical errors fixed. RevTeX, 19 pages, 17 PS figure

Mitochondria and neuroplasticity

The production of neurons from neural progenitor cells, the growth of axons and dendrites and the formation and reorganization of synapses are examples of neuroplasticity. These processes are regulated by cell-autonomous and intercellular (paracrine and endocrine) programs that mediate responses of neural cells to environmental input. Mitochondria are highly mobile and move within and between subcellular compartments involved in neuroplasticity (synaptic terminals, dendrites, cell body and the axon). By generating energy (ATP and NAD+), and regulating subcellular Ca2+ and redox homoeostasis, mitochondria may play important roles in controlling fundamental processes in neuroplasticity, including neural differentiation, neurite outgrowth, neurotransmitter release and dendritic remodelling. Particularly intriguing is emerging data suggesting that mitochondria emit molecular signals (e.g. reactive oxygen species, proteins and lipid mediators) that can act locally or travel to distant targets including the nucleus. Disturbances in mitochondrial functions and signalling may play roles in impaired neuroplasticity and neuronal degeneration in Alzheimer's disease, Parkinson's disease, psychiatric disorders and stroke