317 research outputs found
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
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 -anonymity. This approach requires that the rows of a table
are partitioned in clusters of size at least 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 , and when the records have length at most 8
and . 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 ). 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 -anonymity problem, when restricting the
instance to records having length bounded by 3 and . 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 ; 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 of lattice
QCD in the Hamiltonian approach is investigated. As was shown earlier,
is isomorphic to the tensor product of a gluonic
-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
(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 . Furthermore, we construct three other transformations of
the lattice fields under which the variation of the lattice action vanishes to
where 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
. 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
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