228 research outputs found
Collineation group as a subgroup of the symmetric group
Let be the projectivization (i.e., the set of one-dimensional vector
subspaces) of a vector space of dimension over a field. Let be a
closed (in the pointwise convergence topology) subgroup of the permutation
group of the set . Suppose that contains the
projective group and an arbitrary self-bijection of transforming a
triple of collinear points to a non-collinear triple. It is well-known from
\cite{KantorMcDonough} that if is finite then contains the
alternating subgroup of .
We show in Theorem \ref{density} below that , if
is infinite.Comment: 9 page
Closed String Tachyons and Semi-Classical Instabilities
We conjecture that the end point of bulk closed string tachyon decay at any
non-zero coupling, is the annihilation of space time by Witten's bubble of
nothing, resulting in a topological phase of the theory. In support of this we
present a variety of situations in which there is a correspondence between the
existence of perturbative tachyons in one regime and the semi-classical
annihilation of space-time. Our discussion will include many recently
investigated scenarios in string theory including Scherk-Schwarz
compactifications, Melvin magnetic backgrounds, and noncompact orbifolds. We
use this conjecture to investigate a possible web of dualities relating the
eleven-dimensional Fabinger-Horava background with nonsupersymmetric string
theories. Along the way we point out where our conjecture resolves some of the
puzzles associated with bulk closed string tachyon condensation.Comment: 31 pages, 5 figures 3 figures added, typos corrected and references
added. Discussion of Type 0/Heterotic s-duality extended and some other
points clarified Revision of discussion on Fabinger-Horava string
descendents, section on Scherk-Schwarz compactification of Horava-Witten
removed, some references adde
Models for Enhanced Absorption in Inhomogeneous Superconductors
We discuss the low-frequency absorption arising from quenched inhomogeneity
in the superfluid density rho_s of a model superconductor. Such inhomogeneities
may arise in a high-T_c superconductor from a wide variety of sources,
including quenched random disorder and static charge density waves such as
stripes. Using standard classical methods for treating randomly inhomogeneous
media, we show that both mechanisms produce additional absorption at finite
frequencies. For a two-fluid model with weak mean-square fluctuations <(d
rho_s)^2 > in rho_s and a frequency-independent quasiparticle conductivity, the
extra absorption has oscillator strength proportional to the quantity <(d
rho_s)^2>/rho_s, as observed in some experiments. Similar behavior is found in
a two-fluid model with anticorrelated fluctuations in the superfluid and normal
fluid densities. The extra absorption typically occurs as a Lorentzian centered
at zero frequency. We present simple model calculations for this extra
absorption under conditions of both weak and strong fluctuations. The relation
between our results and other model calculations is briefly discussed
Dualities in Quantum Hall System and Noncommutative Chern-Simons Theory
We discuss different dualities of QHE in the framework of the noncommutative
Chern-Simons theory. First, we consider the Morita or T-duality transformation
on the torus which maps the abelian noncommutative CS description of QHE on the
torus into the nonabelian commutative description on the dual torus. It is
argued that the Ruijsenaars integrable many-body system provides the
description of the QHE with finite amount of electrons on the torus. The new
IIB brane picture for the QHE is suggested and applied to Jain and generalized
hierarchies. This picture naturally links 2d -model and 3d CS
description of the QHE. All duality transformations are identified in the brane
setup and can be related with the mirror symmetry and S duality. We suggest a
brane interpretation of the plateu transition in IQHE in which a critical point
is naturally described by WZW model.Comment: 31 pages, 4 figure
Energy Distribution associated with Static Axisymmetric Solutions
This paper has been addressed to a very old but burning problem of energy in
General Relativity. We evaluate energy and momentum densities for the static
and axisymmetric solutions. This specializes to two metrics, i.e., Erez-Rosen
and the gamma metrics, belonging to the Weyl class. We apply four well-known
prescriptions of Einstein, Landau-Lifshitz, Papaterou and Mller to
compute energy-momentum density components. We obtain that these prescriptions
do not provide similar energy density, however momentum becomes constant in
each case. The results can be matched under particular boundary conditions.Comment: 18 pages, accepted for publication in Astrophysics and SpaceScienc
The Volume of some Non-spherical Horizons and the AdS/CFT Correspondence
We calculate the volumes of a large class of Einstein manifolds, namely
Sasaki-Einstein manifolds which are the bases of Ricci-flat affine cones
described by polynomial embedding relations in C^n. These volumes are important
because they allow us to extend and test the AdS/CFT correspondence. We use
these volumes to extend the central charge calculation of Gubser (1998) to the
generalized conifolds of Gubser, Shatashvili, and Nekrasov (1999). These
volumes also allow one to quantize precisely the D-brane flux of the AdS
supergravity solution. We end by demonstrating a relationship between the
volumes of these Einstein spaces and the number of holomorphic polynomials
(which correspond to chiral primary operators in the field theory dual) on the
corresponding affine cone.Comment: 25 pp, LaTeX, 1 figure, v2: refs adde
World-sheet duality for D-branes with travelling waves
We study D-branes with plane waves of arbitrary profiles as examples of
time-dependent backgrounds in string theory. We show how to reproduce the
quantum mechanical (one-to-one) open-string S-matrix starting from the
closed-string boundary state for the D-branes, thereby establishing the channel
duality of this calculation. The required Wick rotation to a Lorentzian
worldsheet singles out as 'prefered' time coordinate the open-string light-cone
time.Comment: 17 pages, Latex file, uses JHEP3.cls, two figures. Added references
and corrected two typo
D-Brane Probes of Special Holonomy Manifolds
Using D2-brane probes, we study various properties of M-theory on singular,
non-compact manifolds of G_2 and Spin(7) holonomy. We derive mirror pairs of
N=1 supersymmetric three-dimensional gauge theories, and apply this technique
to realize exceptional holonomy manifolds as both Coulomb and Higgs branches of
the D2-brane world-volume theory. We derive a ``G_2 quotient construction'' of
non-compact manifolds which admit a metric of G_2 holonomy. We further discuss
the moduli space of such manifolds, including the structure of geometrical
transitions in each case. For completeness, we also include familiar examples
of manifolds with SU(3) and Sp(2) holonomy, where some of the new ideas are
clarified and tested.Comment: 79 pages, Late
A Measurement of Time-Averaged Aerosol Optical Depth using Air-Showers Observed in Stereo by HiRes
Air fluorescence measurements of cosmic ray energy must be corrected for
attenuation of the atmosphere. In this paper we show that the air-showers
themselves can yield a measurement of the aerosol attenuation in terms of
optical depth, time-averaged over extended periods. Although the technique
lacks statistical power to make the critical hourly measurements that only
specialized active instruments can achieve, we note the technique does not
depend on absolute calibration of the detector hardware, and requires no
additional equipment beyond the fluorescence detectors that observe the air
showers. This paper describes the technique, and presents results based on
analysis of 1258 air-showers observed in stereo by the High Resolution Fly's
Eye over a four year span.Comment: 7 pages, 3 figures, accepted for publication by Astroparticle Physics
Journa
Search for Global Dipole Enhancements in the HiRes-I Monocular Data above 10^{18.5} eV
Several proposed source models for Ultra-High Energy Cosmic Rays (UHECRs)
consist of dipole distributions oriented towards major astrophysical landmarks
such as the galactic center, M87, or Centaurus A. We use a comparison between
real data and simulated data to show that the HiRes-I monocular data for
energies above 10^{18.5} eV is, in fact, consistent with an isotropic source
model. We then explore methods to quantify our sensitivity to dipole source
models oriented towards the Galactic Center, M87, and Centaurus A.Comment: 17 pages, 31 figure
- …