Scaling in the Positive Plaquette Model and Universality in SU(2) Lattice Gauge Theory

We investigate universality, scaling, the beta-function and the topological charge in the positive plaquette model for SU(2) lattice gauge theory. Comparing physical quantities, like the critical temperature, the string tension, glueball masses, and their ratios, we explore the effect of a complete suppression of a certain lattice artifact, namely the negative plaquettes, for SU(2) lattice gauge theory. Our result is that this modification does not change the continuum limit, i.e., the universality class. The positive plaquette model and the standard Wilson formulation describe the same physical situation. The approach to the continuum limit given by the beta-function in terms of the bare lattice coupling, however, is rather different: the beta-function of the positive plaquette model does not show a dip like the model with standard Wilson action.Comment: 35 pages, preprint numbers FSU-SCRI-94-71 and HU Berlin-IEP-94/1

Monopole clusters in Abelian projected gauge theories

We show that the monopole currents which one obtains in the maximally Abelian gauge of SU(2) fall into two quite distinct classes (when the volume is large enough). In each field configuration there is precisely one cluster that permeates the whole lattice volume. It has a current density and a magnetic screening mass that scale and it produces the whole of the string tension. The remaining clusters have a number density that follows an approximate power law proportional to the inverse cube of l where l is the length of the monopole world line in lattice units. These clusters are localised in space-time with radii which vary as the square root of l. In terms of the radius r these `lumps' have a scale-invariant distribution proportional to (dr/r . 1/{r^4}). Moreover they appear not to contribute at all to the string tension. The fact that they are scale-invariant at small distances would seem to rule out an instanton origin.Comment: LaTeX, 31 pages, 11 PostScript figures. Typo in Table 2 correcte

A Magnetic Monopole in Pure SU(2) Gauge Theory

The magnetic monopole in euclidean pure SU(2) gauge theory is investigated using a background field method on the lattice. With Monte Carlo methods we study the mass of the monopole in the full quantum theory. The monopole background under the quantum fluctuations is induced by imposing fixed monopole boundary conditions on the walls of a finite lattice volume. By varying the gauge coupling it is possible to study monopoles with scales from the hadronic scale up to high energies. The results for the monopole mass are consistent with a conjecture we made previously in a realization of the dual superconductor hypothesis of confinement.Comment: 33 pages uufiles-compressed PostScript including (all) 12 figures, preprint numbers ITFA-93-19 (Amsterdam), OUTP-93-21P (Oxford), DFTUZ/93/23 (Zaragoza

Topological Structure of the SU(3) Vacuum

We investigate the topological structure of the vacuum in SU(3) lattice gauge theory. We use under-relaxed cooling to remove the high-frequency fluctuations and a variety of "filters" to identify the topological charges in the resulting smoothened field configurations. We find a densely packed vacuum with an average instanton size, in the continuum limit, of about 0.5 fm. The density at large sizes decreases as a large inverse power of the size. At small sizes we see some sign of a trend towards the asymptotic perturbative behaviour. We find that an interesting polarisation phenomenon occurs: the large topological charges tend to have, on the average, the same sign and are over-screened by the smaller charges which tend to have, again on the average, the opposite sign to the larger instantons. We also calculate the topological susceptibility for which we obtain a continuum value of about 187 MeV. We perform the calculations for various volumes, lattice spacings and numbers of cooling sweeps, so as to obtain some control over the associated systematic errors. The coupling range is from beta=6.0 to beta=6.4 and the lattice volumes range from 16x16x16x48 to 32x32x32x64.Comment: LaTeX. Self-unpacking, uuencoded tar-compressed fil

The Hyperfine Splitting in Charmonium: Lattice Computations Using the Wilson and Clover Fermion Actions

We compute the hyperfine splitting $m_{J/\psi}-m_{\eta_c}$ on the lattice, using both the Wilson and $O(a)$-improved (clover) actions for quenched quarks. The computations are performed on a $24^3\times48$ lattice at $\beta = 6.2$, using the same set of 18 gluon configurations for both fermion actions. We find that the splitting is 1.83\err{13}{15} times larger with the clover action than with the Wilson action, demonstrating the sensitivity of the spin-splitting to the magnetic moment term which is present in the clover action. However, even with the clover action the result is less than half of the physical mass-splitting. We also compute the decay constants $f_{\eta_c}$ and $f^{-1}_{J/\psi}$, both of which are considerably larger when computed using the clover action than with the Wilson action. For example for the ratio $f^{-1}_{J/\psi}/f^{-1}_{\rho}$ we find 0.32\err{1}{2} with the Wilson action and $0.48\pm 3$ with the clover action (the physical value is 0.44(2)).Comment: LaTeX file, 8 pages and two postscript figures. Southampton Preprint: SHEP 91/92-27 Edinburgh Preprint: 92/51

Behavioral responses of the endemic shrimp Halocardina rubra (Malacostraca:Atyidae) to an introduced fish, Gambusia affinis (Actinopterygii: Poeciliidae) and implications for the trophic structure of Hawaiian anchialine ponds

In the Hawaiian Islands, intentionally introduced exotic fishes have been linked to changes in native biodiversity and community composition. In 1905, the mosquito fish Gambusia affinis was introduced to control mosquitoes. Subsequently, G. affinis spread throughout the Islands and into coastal anchialine ponds. Previous studies suggest that presence of invasive fishes in anchialine ponds may eliminate native species, including the endemic shrimp Halocaridina rubra. We examined effects of G. affinis on H. rubra populations in anchialine ponds on the Kona-Kohala coast of the island of Hawai/i. In the presence of G. affinis, H. rubra exhibited a diel activity pattern that was not seen in fishless ponds. Shrimp in ponds with fish were active only at night. This pattern was evident in anchialine ponds and in laboratory experiments. In laboratory predation experiments, G. affinis preferentially consumed smaller H. rubra, and in the field the H. rubra collected from invaded sites were larger than those from fishless ponds. Analysis of trophic position using stable isotope analyses showed that feeding of H. rubra was not significantly distinct from that of snails, assumed to feed at trophic level 2.0 on epilithic algae, but G. affinis was slightly omnivorous, feeding at tropic level 2.2. The mosquito fish diet was apparently composed primarily of algae when the defensive behavior of H. rubra made them substantially unavailable as prey. The effect of successful establishment of G. affinis on shrimp behavior has the potential to alter abundance of benthic algae and processing and recycling of nutrients in anchialine pond ecosystems

Tadpole-improved SU(2) lattice gauge theory

A comprehensive analysis of tadpole-improved SU(2) lattice gauge theory is made. Simulations are done on isotropic and anisotropic lattices, with and without improvement. Two tadpole renormalization schemes are employed, one using average plaquettes, the other using mean links in Landau gauge. Simulations are done with spatial lattice spacings $a_s$ in the range of about 0.1--0.4 fm. Results are presented for the static quark potential, the renormalized lattice anisotropy $a_t/a_s$ (where $a_t$ is the ``temporal'' lattice spacing), and for the scalar and tensor glueball masses. Tadpole improvement significantly reduces discretization errors in the static quark potential and in the scalar glueball mass, and results in very little renormalization of the bare anisotropy that is input to the action. We also find that tadpole improvement using mean links in Landau gauge results in smaller discretization errors in the scalar glueball mass (as well as in the static quark potential), compared to when average plaquettes are used. The possibility is also raised that further improvement in the scalar glueball mass may result when the coefficients of the operators which correct for discretization errors in the action are computed beyond tree level.Comment: 14 pages, 7 figures (minor changes to overall scales in Fig.1; typos removed from Eqs. (3),(4),(15); some rewording of Introduction

Implementing an electronic sideband offset lock for precision spectroscopy in radium

We demonstrate laser frequency stabilization with at least 6 GHz of offset tunability using an in-phase/quadrature (IQ) modulator to generate electronic sidebands (ESB) on a titanium sapphire laser at 714 nm and we apply this technique to the precision spectroscopy of $^{226}$Ra, and $^{225}$Ra. By locking the laser to a single resonance of a high finesse optical cavity and adjusting the lock offset, we determine the frequency difference between the magneto-optical trap (MOT) transitions in the two isotopes to be $2630.0\pm0.3$ MHz, a factor of 29 more precise than the previously available data. Using the known value of the hyperfine splitting of the $^{3}P_{1}$ level, we calculate the isotope shift for the $^{1}S_{0}$ to $^{3}P_{1}$ transition to be $2267.0\pm2.2$ MHz, which is a factor of 8 more precise than the best available value. Our technique could be applied to countless other atomic systems to provide unprecedented precision in isotope shift spectroscopy and other relative frequency comparisons

Janus Black Holes

In this paper Janus black holes in AdS3 are considered. These are static solutions of an Einstein-scalar system with broken translation symmetry along the horizon. These solutions are dual to interface conformal field theories at finite temperature. An approximate solution is first constructed using perturbation theory around a planar BTZ black hole. Numerical and exact solutions valid for all sets of parameters are then found and compared. Using the exact solution the thermodynamics of the system is analyzed. The entropy associated with the Janus black hole is calculated and it is found that the entropy of the black Janus is the sum of the undeformed black hole entropy and the entanglement entropy associated with the defect.Comment: 28 pages, 2 figures, reference adde