671 research outputs found
Open orbifold Gromov-Witten invariants of [C^3/Z_n]: localization and mirror symmetry
We develop a mathematical framework for the computation of open orbifold
Gromov-Witten invariants of [C^3/Z_n], and provide extensive checks with
predictions from open string mirror symmetry. To this aim we set up a
computation of open string invariants in the spirit of Katz-Liu, defining them
by localization. The orbifold is viewed as an open chart of a global quotient
of the resolved conifold, and the Lagrangian as the fixed locus of an
appropriate anti-holomorphic involution. We consider two main applications of
the formalism. After warming up with the simpler example of [C^3/Z_3], where we
verify physical predictions of Bouchard, Klemm, Marino and Pasquetti, the main
object of our study is the richer case of [C^3/Z_4], where two different
choices are allowed for the Lagrangian. For one choice, we make numerical
checks to confirm the B-model predictions; for the other, we prove a mirror
theorem for orbifold disc invariants, match a large number of annulus
invariants, and give mirror symmetry predictions for open string invariants of
genus \leq 2.Comment: 44 pages + appendices; v2: exposition improved, misprints corrected,
version to appear on Selecta Mathematica; v3: last minute mistake found and
fixed for the symmetric brane setup of [C^3/Z_4]; in pres
Introduction to Arithmetic Mirror Symmetry
We describe how to find period integrals and Picard-Fuchs differential
equations for certain one-parameter families of Calabi-Yau manifolds. These
families can be seen as varieties over a finite field, in which case we show in
an explicit example that the number of points of a generic element can be given
in terms of p-adic period integrals. We also discuss several approaches to
finding zeta functions of mirror manifolds and their factorizations. These
notes are based on lectures given at the Fields Institute during the thematic
program on Calabi-Yau Varieties: Arithmetic, Geometry, and Physics
Orthorhombically Mixed s and d Wave Superconductivity and Josephson Tunneling
The effect of orthorhombicity on Josephson tunneling in high T
superconductors such as YBCO is studied for both single crystals and highly
twinned crystals. It is shown that experiments on highly twinned crystals
experimentally determine the symmetry of the superconducting twin boundaries
(which can be either even or odd with respect to a reflection in the twinning
plane). Conversely, Josephson experiments on highly twinned crystals can not
experimentally determine whether the superconductivity is predominantly
-wave or predominantly -wave. The direct experimental determination of
the order-parameter symmetry by Josephson tunneling in YBCO thus comes from the
relatively few experiments which have been carried out on untwinned single
crystals.Comment: 5 pages, RevTeX file, 1 figure available on request
([email protected]
Remodeling the B-model
We propose a complete, new formalism to compute unambiguously B-model open
and closed amplitudes in local Calabi-Yau geometries, including the mirrors of
toric manifolds. The formalism is based on the recursive solution of matrix
models recently proposed by Eynard and Orantin. The resulting amplitudes are
non-perturbative in both the closed and the open moduli. The formalism can then
be used to study stringy phase transitions in the open/closed moduli space. At
large radius, this formalism may be seen as a mirror formalism to the
topological vertex, but it is also valid in other phases in the moduli space.
We develop the formalism in general and provide an extensive number of checks,
including a test at the orbifold point of A_p fibrations, where the amplitudes
compute the 't Hooft expansion of Wilson loops in lens spaces. We also use our
formalism to predict the disk amplitude for the orbifold C^3/Z_3.Comment: 83 pages, 9 figure
Flat Information Geometries in Black Hole Thermodynamics
The Hessian of either the entropy or the energy function can be regarded as a
metric on a Gibbs surface. For two parameter families of asymptotically flat
black holes in arbitrary dimension one or the other of these metrics are flat,
and the state space is a flat wedge. The mathematical reason for this is traced
back to the scale invariance of the Einstein-Maxwell equations. The picture of
state space that we obtain makes some properties such as the occurence of
divergent specific heats transparent.Comment: 14 pages, one figure. Dedicated to Rafael Sorkin's birthda
An exact solution of the moving boundary problem for the relativistic plasma expansion in a dipole magnetic field
An exact analytic solution is obtained for a uniformly expanding, neutral,
highly conducting plasma sphere in an ambient dipole magnetic field with an
arbitrary orientation of the dipole moment in the space. Based on this solution
the electrodynamical aspects related to the emission and transformation of
energy have been considered. In order to highlight the effect of the
orientation of the dipole moment in the space we compare our results obtained
for parallel orientation with those for transversal orientation. The results
obtained can be used to treat qualitatively experimental and simulation data,
and several phenomena of astrophysical and laboratory significance.Comment: 7 pages, 2 figures. arXiv admin note: substantial text overlap with
arXiv:physics/060323
Harrison transformation of hyperelliptic solutions and charged dust disks
We use a Harrison transformation on solutions to the stationary axisymmetric
Einstein equations to generate solutions of the Einstein-Maxwell equations. The
case of hyperelliptic solutions to the Ernst equation is studied in detail.
Analytic expressions for the metric and the multipole moments are obtained. As
an example we consider the transformation of a family of counter-rotating dust
disks. The resulting solutions can be interpreted as disks with currents and
matter with a purely azimuthal pressure or as two streams of freely moving
charged particles. We discuss interesting limiting cases as the extreme limit
where the charge becomes identical to the mass, and the ultrarelativistic limit
where the central redshift diverges.Comment: 20 pages, 9 figure
Efficiency of the dynamical mechanism
The most extreme starbursts occur in galaxy mergers, and it is now
acknowledged that dynamical triggering has a primary importance in star
formation. This triggering is due partly to the enhanced velocity dispersion
provided by gravitational instabilities, such as density waves and bars, but
mainly to the radial gas flows they drive, allowing large amounts of gas to
condense towards nuclear regions in a small time scale. Numerical simulations
with several gas phases, taking into account the feedback to regulate star
formation, have explored the various processes, using recipes like the Schmidt
law, moderated by the gas instability criterion. May be the most fundamental
parameter in starbursts is the availability of gas: this sheds light on the
amount of external gas accretion in galaxy evolution. The detailed mechanisms
governing gas infall in the inner parts of galaxy disks are discussed.Comment: 6 pages, 3 figures, to be published in "Starbursts - From 30 Doradus
to Lyman break galaxies", ed. R. de Grijs and R. Gonzalez-Delgad
C^2/Z_n Fractional branes and Monodromy
We construct geometric representatives for the C^2/Z_n fractional branes in
terms of branes wrapping certain exceptional cycles of the resolution. In the
process we use large radius and conifold-type monodromies, and also check some
of the orbifold quantum symmetries. We find the explicit Seiberg-duality which
connects our fractional branes to the ones given by the McKay correspondence.
We also comment on the Harvey-Moore BPS algebras.Comment: 34 pages, v1 identical to v2, v3: typos fixed, discussion of
Harvey-Moore BPS algebras update
The Quantum McKay Correspondence for polyhedral singularities
Let G be a polyhedral group, namely a finite subgroup of SO(3). Nakamura's
G-Hilbert scheme provides a preferred Calabi-Yau resolution Y of the polyhedral
singularity C^3/G. The classical McKay correspondence describes the classical
geometry of Y in terms of the representation theory of G. In this paper we
describe the quantum geometry of Y in terms of R, an ADE root system associated
to G. Namely, we give an explicit formula for the Gromov-Witten partition
function of Y as a product over the positive roots of R. In terms of counts of
BPS states (Gopakumar-Vafa invariants), our result can be stated as a
correspondence: each positive root of R corresponds to one half of a genus zero
BPS state. As an application, we use the crepant resolution conjecture to
provide a full prediction for the orbifold Gromov-Witten invariants of [C^3/G].Comment: Introduction rewritten. Issue regarding non-uniqueness of conifold
resolution clarified. Version to appear in Inventione
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