370 research outputs found
Topics on the geometry of D-brane charges and Ramond-Ramond fields
In this paper we discuss some topics on the geometry of type II superstring
backgrounds with D-branes, in particular on the geometrical meaning of the
D-brane charge, the Ramond-Ramond fields and the Wess-Zumino action. We see
that, depending on the behaviour of the D-brane on the four non-compact
space-time directions, we need different notions of homology and cohomology to
discuss the associated fields and charge: we give a mathematical definition of
such notions and show their physical applications. We then discuss the problem
of corretly defining Wess-Zumino action using the theory of p-gerbes. Finally,
we recall the so-called *-problem and make some brief remarks about it.Comment: 29 pages, no figure
Born-Infeld Theory and Stringy Causality
Fluctuations around a non-trivial solution of Born-Infeld theory have a
limiting speed given not by the Einstein metric but the Boillat metric. The
Boillat metric is S-duality invariant and conformal to the open string metric.
It also governs the propagation of scalars and spinors in Born-Infeld theory.
We discuss the potential clash between causality determined by the closed
string and open string light cones and find that the latter never lie outside
the former. Both cones touch along the principal null directions of the
background Born-Infeld field. We consider black hole solutions in situations in
which the distinction between bulk and brane is not sharp such as space filling
branes and find that the location of the event horizon and the thermodynamic
properties do not depend on whether one uses the closed or open string metric.
Analogous statements hold in the more general context of non-linear
electrodynamics or effective quantum-corrected metrics. We show how Born-Infeld
action to second order might be obtained from higher-curvature gravity in
Kaluza-Klein theory. Finally we point out some intriguing analogies with
Einstein-Schr\"odinger theory.Comment: 31 pages, 4 figures, LaTex; Some comments and references adde
The de Rham homotopy theory and differential graded category
This paper is a generalization of arXiv:0810.0808. We develop the de Rham
homotopy theory of not necessarily nilpotent spaces, using closed dg-categories
and equivariant dg-algebras. We see these two algebraic objects correspond in a
certain way. We prove an equivalence between the homotopy category of schematic
homotopy types and a homotopy category of closed dg-categories. We give a
description of homotopy invariants of spaces in terms of minimal models. The
minimal model in this context behaves much like the Sullivan's minimal model.
We also provide some examples. We prove an equivalence between fiberwise
rationalizations and closed dg-categories with subsidiary data.Comment: 47 pages. final version. The final publication is available at
http://www.springerlink.co
Mathematics of Gravitational Lensing: Multiple Imaging and Magnification
The mathematical theory of gravitational lensing has revealed many generic
and global properties. Beginning with multiple imaging, we review
Morse-theoretic image counting formulas and lower bound results, and
complex-algebraic upper bounds in the case of single and multiple lens planes.
We discuss recent advances in the mathematics of stochastic lensing, discussing
a general formula for the global expected number of minimum lensed images as
well as asymptotic formulas for the probability densities of the microlensing
random time delay functions, random lensing maps, and random shear, and an
asymptotic expression for the global expected number of micro-minima. Multiple
imaging in optical geometry and a spacetime setting are treated. We review
global magnification relation results for model-dependent scenarios and cover
recent developments on universal local magnification relations for higher order
caustics.Comment: 25 pages, 4 figures. Invited review submitted for special issue of
General Relativity and Gravitatio
The detection of Gravitational Waves
This chapter is concerned with the question: how do gravitational waves (GWs)
interact with their detectors? It is intended to be a theory review of the
fundamental concepts involved in interferometric and acoustic (Weber bar) GW
antennas. In particular, the type of signal the GW deposits in the detector in
each case will be assessed, as well as its intensity and deconvolution. Brief
reference will also be made to detector sensitivity characterisation, including
very summary data on current state of the art GW detectors.Comment: 33 pages, 12 figures, LaTeX2e, Springer style files --included. For
Proceedings of the ERE-2001 Conference (Madrid, September 2001
D-brane Deconstructions in IIB Orientifolds
With model building applications in mind, we collect and develop basic
techniques to analyze the landscape of D7-branes in type IIB compact Calabi-Yau
orientifolds, in three different pictures: F-theory, the D7 worldvolume theory
and D9-anti-D9 tachyon condensation. A significant complication is that
consistent D7-branes in the presence of O7^- planes are generically singular,
with singularities locally modeled by the Whitney Umbrella. This invalidates
the standard formulae for charges, moduli space and flux lattice dimensions. We
infer the correct formulae by comparison to F-theory and derive them
independently and more generally from the tachyon picture, and relate these
numbers to the closed string massless spectrum of the orientifold
compactification in an interesting way. We furthermore give concrete recipes to
explicitly and systematically construct nontrivial D-brane worldvolume flux
vacua in arbitrary Calabi-Yau orientifolds, illustrate how to read off D-brane
flux content, enhanced gauge groups and charged matter spectra from tachyon
matrices, and demonstrate how brane recombination in general leads to flux
creation, as required by charge conservation and by equivalence of geometric
and gauge theory moduli spaces.Comment: 49 pages, v2: two references adde
A quantum Monte Carlo study of the one-dimensional ionic Hubbard model
Quantum Monte Carlo methods are used to study a quantum phase transition in a
1D Hubbard model with a staggered ionic potential (D). Using recently
formulated methods, the electronic polarization and localization are determined
directly from the correlated ground state wavefunction and compared to results
of previous work using exact diagonalization and Hartree-Fock. We find that the
model undergoes a thermodynamic transition from a band insulator (BI) to a
broken-symmetry bond ordered (BO) phase as the ratio of U/D is increased. Since
it is known that at D = 0 the usual Hubbard model is a Mott insulator (MI) with
no long-range order, we have searched for a second transition to this state by
(i) increasing U at fixed ionic potential (D) and (ii) decreasing D at fixed U.
We find no transition from the BO to MI state, and we propose that the MI state
in 1D is unstable to bond ordering under the addition of any finite ionic
potential. In real 1D systems the symmetric MI phase is never stable and the
transition is from a symmetric BI phase to a dimerized BO phase, with a
metallic point at the transition
Non-standard embedding and five-branes in heterotic M-Theory
We construct vacua of M-theory on S^1/Z_2 associated with Calabi-Yau
three-folds. These vacua are appropriate for compactification to N=1
supersymmetry theories in both four and five dimensions. We allow for general
E_8 x E_8 gauge bundles and for the presence of five-branes. The five-branes
span the four-dimensional uncompactified space and are wrapped on holomorphic
curves in the Calabi-Yau space. Properties of these vacua, as well as of the
resulting low-energy theories, are discussed. We find that the low-energy gauge
group is enlarged by gauge fields that originate on the five-brane
world-volumes. In addition, the five-branes increase the types of new E_8 x E_8
breaking patterns allowed by the non-standard embedding. Characteristic
features of the low-energy theory, such as the threshold corrections to the
gauge kinetic functions, are significantly modified due to the presence of the
five-branes, as compared to the case of standard or non-standard embeddings
without five-branes.Comment: 34 pages, Latex 2e with amsmath, typos removed, factors corrected,
refs improve
Energy Flow in the Hadronic Final State of Diffractive and Non-Diffractive Deep-Inelastic Scattering at HERA
An investigation of the hadronic final state in diffractive and
non--diffractive deep--inelastic electron--proton scattering at HERA is
presented, where diffractive data are selected experimentally by demanding a
large gap in pseudo --rapidity around the proton remnant direction. The
transverse energy flow in the hadronic final state is evaluated using a set of
estimators which quantify topological properties. Using available Monte Carlo
QCD calculations, it is demonstrated that the final state in diffractive DIS
exhibits the features expected if the interaction is interpreted as the
scattering of an electron off a current quark with associated effects of
perturbative QCD. A model in which deep--inelastic diffraction is taken to be
the exchange of a pomeron with partonic structure is found to reproduce the
measurements well. Models for deep--inelastic scattering, in which a
sizeable diffractive contribution is present because of non--perturbative
effects in the production of the hadronic final state, reproduce the general
tendencies of the data but in all give a worse description.Comment: 22 pages, latex, 6 Figures appended as uuencoded fil
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