Exact lattice Ward-Takahashi identity for the N=1 Wess-Zumino model

We consider a lattice formulation of the four dimensional N=1 Wess-Zumino model that uses the Ginsparg-Wilson relation. This formulation has an exact supersymmetry on the lattice. We show that the corresponding Ward-Takahashi identity is satisfied, both at fixed lattice spacing and in the continuum limit. The calculation is performed in lattice perturbation theory up to order $g^2$ in the coupling constant. We also show that this Ward-Takahashi identity determines the finite part of the scalar and fermion renormalization wave functions which automatically leads to restoration of supersymmetry in the continuum limit. In particular, these wave functions coincide in this limit.Comment: 19 pages, 6 figure

Perturbative Study of the Supersymmetric Lattice Theory from Matrix Model

We study the lattice model for the supersymmetric Yang-Mills theory in two dimensions proposed by Cohen, Kaplan, Katz, and Unsal. We re-examine the formal proof for the absence of susy breaking counter terms as well as the stability of the vacuum by an explicit perturbative calculation for the case of U(2) gauge group. Introducing fermion masses and treating the bosonic zero momentum mode nonperturbatively, we avoid the infra-red divergences in the perturbative calculation. As a result, we find that there appear mass counter terms for finite volume which vanish in the infinite volume limit so that the theory needs no fine-tuning. We also find that the supersymmetry plays an important role in stabilizing the lattice space-time by the deconstruction.Comment: 36 pages, 18 figures; typos corrected, some definitions added, appendix including feynman dyagram delete

Relativistic Beaming and the Intrinsic Properties of Extragalactic Radio Jets

Relations between the observed quantities for a beamed radio jet, apparent transverse speed and apparent luminosity (beta_app,L), and the intrinsic quantities, Lorentz factor and intrinsic luminosity (gamma,L_o), are investigated. The inversion from measured to intrinsic values is not unique, but approximate limits to gamma and L_o can be found using probability arguments. Roughly half the sources in a flux density--limited, beamed sample have a value of gamma close to the measured beta_app. The methods are applied to observations of 119 AGN jets made with the VLBA at 15 GHz during 1994-2002. The results strongly support the common relativistic beam model for an extragalactic radio jet. The (beta_app,L) data are closely bounded by a theoretical envelope, an aspect curve for gamma=32, L_o= 10^25 W/Hz. This gives limits to the maximum values of gamma and L_o in the sample: gamma_max about 32, and L_o,max ~ 10^26 W/Hz. No sources with both high beta_app and low L are observed. This is not the result of selection effects due to the observing limits, which are flux density S>0.5 Jy, and angular velocity mu<4 mas/yr. Many of the fastest quasars have a pattern Lorentz factor gamma_p close to that of the beam, gamma_b, but some of the slow quasars must have gamma_p<<gamma_b. Three of the 10 galaxies in the sample have a superluminal feature, with speeds up to beta_app about 6. The others are at most mildly relativistic. The galaxies are not off-axis versions of the powerful quasars, but Cygnus A might be an exception.Comment: 12 pages, 9 figures, 1 table, accepted for publication in the Astrophysical Journa

Parameterized Complexity of the k-anonymity Problem

The problem of publishing personal data without giving up privacy is becoming increasingly important. An interesting formalization that has been recently proposed is the $k$-anonymity. This approach requires that the rows of a table are partitioned in clusters of size at least $k$ and that all the rows in a cluster become the same tuple, after the suppression of some entries. The natural optimization problem, where the goal is to minimize the number of suppressed entries, is known to be APX-hard even when the records values are over a binary alphabet and $k=3$, and when the records have length at most 8 and $k=4$ . In this paper we study how the complexity of the problem is influenced by different parameters. In this paper we follow this direction of research, first showing that the problem is W[1]-hard when parameterized by the size of the solution (and the value $k$). Then we exhibit a fixed parameter algorithm, when the problem is parameterized by the size of the alphabet and the number of columns. Finally, we investigate the computational (and approximation) complexity of the $k$-anonymity problem, when restricting the instance to records having length bounded by 3 and $k=3$. We show that such a restriction is APX-hard.Comment: 22 pages, 2 figure

AGN Black Hole Masses and Bolometric Luminosities

Black hole mass, along with mass accretion rate, is a fundamental property of active galactic nuclei. Black hole mass sets an approximate upper limit to AGN energetics via the Eddington limit. We collect and compare all AGN black hole mass estimates from the literature; these 177 masses are mostly based on the virial assumption for the broad emission lines, with the broad-line region size determined from either reverberation mapping or optical luminosity. We introduce 200 additional black hole mass estimates based on properties of the host galaxy bulges, using either the observed stellar velocity dispersion or using the fundamental plane relation to infer $\sigma$; these methods assume that AGN hosts are normal galaxies. We compare 36 cases for which black hole mass has been generated by different methods and find, for individual objects, a scatter as high as a couple of orders of magnitude. The less direct the method, the larger the discrepancy with other estimates, probably due to the large scatter in the underlying correlations assumed. Using published fluxes, we calculate bolometric luminosities for 234 AGNs and investigate the relation between black hole mass and luminosity. In contrast to other studies, we find no significant correlation of black hole mass with luminosity, other than those induced by circular reasoning in the estimation of black hole mass. The Eddington limit defines an approximate upper envelope to the distribution of luminosities, but the lower envelope depends entirely on the sample of AGN included. For any given black hole mass, there is a range in Eddington ratio of up to three orders of magnitude.Comment: 43 pages with 10 figures. Accepted for publication in Ap

On the Structure of the Observable Algebra of QCD on the Lattice

The structure of the observable algebra ${\mathfrak O}_{\Lambda}$ of lattice QCD in the Hamiltonian approach is investigated. As was shown earlier, ${\mathfrak O}_{\Lambda}$ is isomorphic to the tensor product of a gluonic $C^{*}$-subalgebra, built from gauge fields and a hadronic subalgebra constructed from gauge invariant combinations of quark fields. The gluonic component is isomorphic to a standard CCR algebra over the group manifold SU(3). The structure of the hadronic part, as presented in terms of a number of generators and relations, is studied in detail. It is shown that its irreducible representations are classified by triality. Using this, it is proved that the hadronic algebra is isomorphic to the commutant of the triality operator in the enveloping algebra of the Lie super algebra ${\rm sl(1/n)}$ (factorized by a certain ideal).Comment: 33 page

A lattice study of the two-dimensional Wess Zumino model

We present results from a numerical simulation of the two-dimensional Euclidean Wess-Zumino model. In the continuum the theory possesses N=1 supersymmetry. The lattice model we employ was analyzed by Golterman and Petcher in \cite{susy} where a perturbative proof was given that the continuum supersymmetric Ward identities are recovered without finite tuning in the limit of vanishing lattice spacing. Our simulations demonstrate the existence of important non-perturbative effects in finite volumes which modify these conclusions. It appears that in certain regions of parameter space the vacuum state can contain solitons corresponding to field configurations which interpolate between different classical vacua. In the background of these solitons supersymmetry is partially broken and a light fermion mode is observed. At fixed coupling the critical mass separating phases of broken and unbroken supersymmetry appears to be volume dependent. We discuss the implications of our results for continuum supersymmetry breaking.Comment: 32 pages, 12 figure

Exact Lattice Supersymmetry: the Two-Dimensional N=2 Wess-Zumino Model

We study the two-dimensional Wess-Zumino model with extended N=2 supersymmetry on the lattice. The lattice prescription we choose has the merit of preserving {\it exactly} a single supersymmetric invariance at finite lattice spacing $a$. Furthermore, we construct three other transformations of the lattice fields under which the variation of the lattice action vanishes to $O(ga^2)$ where $g$ is a typical interaction coupling. These four transformations correspond to the two Majorana supercharges of the continuum theory. We also derive lattice Ward identities corresponding to these exact and approximate symmetries. We use dynamical fermion simulations to check the equality of the massgaps in the boson and fermion sectors and to check the lattice Ward identities. At least for weak coupling we see no problems associated with a lack of reflection positivity in the lattice action and find good agreement with theory. At strong coupling we provide evidence that problems associated with a lack of reflection positivity are evaded for small enough lattice spacing.Comment: 29 pages, 10 figures. New results at strong coupling added. Minor corrections to text and one reference added. Version to appear in Phys. Rev.

A Viewing Angle - Kinetic Luminosity Unification Scheme For BL Lacertae Objects

We propose a unified classification for BL Lac objects (BLs), focusing on the synchrotron peak frequency of the spectral energy distribution. The unification scheme is based on the angle Theta that describes the orientation of the relativistic jet and on the electron kinetic luminosity Lambda of the jet. We assume that Lambda scales with the size of the jet r in a self-similar fashion (Lambda propto r^2), as supported by observational data. The jets are self-similar in geometry and have the same pressure and median magnetic field at the inlet, independent of size. The self-similarity is broken for the highest energy electrons, which radiate mainly at high frequencies, since for large sources they suffer more severe radiative energy losses over a given fraction of the jet length. We calculate the optically thin synchrotron spectrum using an accelerating inner jet model based on simple relativistic gas dynamics and show that it can fit the observed infrared to X-ray spectrum of PKS 2155--304. We couple the accelerating jet model to the unification scheme and compare the results to complete samples of BLs. The negative apparent evolution of X-ray selected BLs is explained as a result of positive evolution of the jet electron kinetic luminosity $\Lambda_{kin}$. We review observational arguments in favor of the existence of scaled-down accretion disks and broad emission-line regions in BLs. The proposed unification scheme can explain the lack of observed broad emission lines in X-ray selected BLs, as well as the existence of those lines preferentially in luminous radio-selected BLs. Finally, we review observational arguments that suggest the extension of this unification scheme to all blazars.Comment: 32 pages, 8 figures, to be published in the ApJ (Oct 20, 1998