On the Isomorphic Description of Chiral Symmetry Breaking by Non-Unitary Lie Groups

It is well-known that chiral symmetry breaking ($\chi$SB) in QCD with $N_{f}=2$ light quark flavours can be described by orthogonal groups as $O(4) \to O(3)$, due to local isomorphisms. Here we discuss the question how specific this property is. We consider generalised forms of $\chi$SB involving an arbitrary number of light flavours of continuum or lattice fermions, in various representations. We search systematically for isomorphic descriptions by non-unitary, compact Lie groups. It turns out that there are a few alternative options in terms of orthogonal groups, while we did not find any description entirely based on symplectic or exceptional Lie groups. If we adapt such an alternative as the symmetry breaking pattern for a generalised Higgs mechanism, we may consider a Higgs particle composed of bound fermions and trace back the mass generation to $\chi$SB. In fact, some of the patterns that we encounter appear in technicolour models. In particular if one observes a Higgs mechanism that can be expressed in terms of orthogonal groups, we specify in which cases it could also represent some kind of $\chi$SB of techniquarks.Comment: 18 pages, to appear in Int. J. Mod. Phys.

Finite-size scaling for the left-current correlator with non-degenerate quark masses

We study the volume dependence of the left-current correlator with non-degenerate quark masses to next-to-leading order in the chiral expansion. We consider three possible regimes: all quark masses are in the $\epsilon$-regime, all are in the $p$-regime and a mixed-regime where the lighest quark masses satisfy $m_v \Sigma V \leq 1$ while the heavier $m_s \Sigma V \gg 1$. These results can be used to match lattice QCD and the Chiral Effective Theory in a large but finite box in which the Compton wavelength of the lightest pions is of the order of the box size. We consider both the full and partially-quenched results.Comment: 27 pages, 4 figure

Lattice Fluid Dynamics from Perfect Discretizations of Continuum Flows

We use renormalization group methods to derive equations of motion for large scale variables in fluid dynamics. The large scale variables are averages of the underlying continuum variables over cubic volumes, and naturally live on a lattice. The resulting lattice dynamics represents a perfect discretization of continuum physics, i.e. grid artifacts are completely eliminated. Perfect equations of motion are derived for static, slow flows of incompressible, viscous fluids. For Hagen-Poiseuille flow in a channel with square cross section the equations reduce to a perfect discretization of the Poisson equation for the velocity field with Dirichlet boundary conditions. The perfect large scale Poisson equation is used in a numerical simulation, and is shown to represent the continuum flow exactly. For non-square cross sections we use a numerical iterative procedure to derive flow equations that are approximately perfect.Comment: 25 pages, tex., using epsfig, minor changes, refernces adde

Spectral Properties of the Overlap Dirac Operator in QCD

We discuss the eigenvalue distribution of the overlap Dirac operator in quenched QCD on lattices of size 8^{4}, 10^{4} and 12^{4} at \beta = 5.85 and \beta = 6. We distinguish the topological sectors and study the distributions of the leading non-zero eigenvalues, which are stereographically mapped onto the imaginary axis. Thus they can be compared to the predictions of random matrix theory applied to the \epsilon-expansion of chiral perturbation theory. We find a satisfactory agreement, if the physical volume exceeds about (1.2 fm)^{4}. For the unfolded level spacing distribution we find an accurate agreement with the random matrix conjecture on all volumes that we considered.Comment: 16 pages, 8 figures, final version published in JHE

Nucleon structure in terms of OPE with non-perturbative Wilson coefficients

Lattice calculations could boost our understanding of Deep Inelastic Scattering by evaluating moments of the Nucleon Structure Functions. To this end we study the product of electromagnetic currents between quark states. The Operator Product Expansion (OPE) decomposes it into matrix elements of local operators (depending on the quark momenta) and Wilson coefficients (as functions of the larger photon momenta). For consistency with the matrix elements, we evaluate a set of Wilson coefficients non-perturbatively, based on propagators for numerous momentum sources, on a 24^3 x 48 lattice. The use of overlap quarks suppresses unwanted operator mixing and lattice artifacts. Results for the leading Wilson coefficients are extracted by means of Singular Value Decomposition.Comment: 7 pages, 3 figures, contribution to the XXVI International Symposium on Lattice Field Theory, July 14-19 Williamsburg, Virginia, US

SN1993J VLBI (I): The Center of the Explosion and a Limit on Anisotropic Expansion

Phase-referenced VLBI observations of supernova 1993J at 24 epochs, from 50 days after shock breakout to the present, allowed us to determine the coordinates of the explosion center relative to the quasi-stationary core of the host galaxy M81 with an accuracy of 45 micro-arcsec, and to determine the nominal proper motion of the geometric center of the radio shell with an accuracy of 9micro-arcsec/yr. The uncertainties correspond to 160 AU for the position and 160 km/s for the proper motion at the distance of the source of 3.63 Mpc. After correcting for the expected galactic proper motion of the supernova around the core of M81 using HI rotation curves, we obtain a peculiar proper motion of the radio shell center of only 320 +/- 160 km/s to the south, which limits any possible one-sided expansion of the shell. We also find that the shell is highly circular, the outer contours in fact being circular to within 3%. Combining our proper motion values with the degree of circular symmetry, we find that the expansion of the shockfront from the explosion center is isotropic to within 5.5% in the plane of the sky. This is a more fundamental result on isotropic expansion than can be derived from the circularity of the images alone. The brightness of the radio shell, however, varies along the ridge and systematically changes with time. The degree of isotropy in the expansion of the shockfront contrasts with the asymmetries and polarization found in optical spectral lines. Asymmetric density distributions in the ejecta or more likely in the circumstellar medium, are favored to reconcile the radio and optical results. We see no sign of any disk-like density distribution of the circumstellar material, with the average axis ratio of the radio shell of SN1993J being less than 1.04.Comment: 21 pages, LaTex + 5 Figures (encapulsated PostScript), Accepted for Publication in the Astrophysical Journa

Indication of Anisotropy in Electromagnetic Propagation over Cosmological Distances

We report a systematic rotation of the plane of polarization of electromagnetic radiation propagating over cosmological distances. The effect is extracted independently from Faraday rotation, and found to be correlated with the angular positions and distances to the sources. Monte Carlo analysis yields probabilistic P-values of order 10^(-3) for this to occur as a fluctuation. A fit yields a birefringence scale of order 10^(25) meters. Dependence on redshift z rules out a local effect. Barring hidden systematic bias in the data, the correlation indicates a new cosmological effect.Comment: 5 pages, 1 figure, ReVTeX. For more information, see http://www.cc.rochester.edu/college/rtc/Borge/aniso.htm

Blocking of lattice monopoles from the continuum in hot lattice gluodynamics

The Abelian monopoles in lattice gluodynamics are associated with continuum monopoles blocked to the lattice. This association allows to predict the lattice monopole action and density of the (squared) monopole charges from a continuum monopole model. The method is applied to the static monopoles in high temperature gluodynamics. We show that the numerical data both for the density and the action of the lattice monopoles can be described in terms of a Coulomb gas of Abelian monopoles in the continuum.Comment: 23 pages, 9 EPS figures, LaTeX2e uses JHEP3 class file; replaced to match published versio

Matrix models and QCD with chemical potential

The Random Matrix Model approach to Quantum Chromodynamics (QCD) with non-vanishing chemical potential is reviewed. The general concept using global symmetries is introduced, as well as its relation to field theory, the so-called epsilon regime of chiral Perturbation Theory (echPT). Two types of Matrix Model results are distinguished: phenomenological applications leading to phase diagrams, and an exact limit of the QCD Dirac operator spectrum matching with echPT. All known analytic results for the spectrum of complex and symplectic Matrix Models with chemical potential are summarised for the symmetry classes of ordinary and adjoint QCD, respectively. These include correlation functions of Dirac operator eigenvalues in the complex plane for real chemical potential, and in the real plane for imaginary isospin chemical potential. Comparisons of these predictions to recent Lattice simulations are also discussed

A variant approach to the overlap action

I describe an implementation of the overlap action, which is built from an action which is itself an approximate overlap action. It appears to be about a factor of 15-20 less expensive to use, than the usual overlap action with the Wilson fermion action as its kernel. Ingredients include a fat link to suppress coupling to dislocations and a free field action with a spectrum which resembles an overlap; much of the gain comes from the use of eigenmodes of the approximate action to begin the overlap calculation. As a physics example, I compute the quark condensate in finite volume in the quenched approximation.Comment: 15 pages, Revtex, postscript figures. COLO-HEP-44