7,576 research outputs found
Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry
Assuming the standard framework of mirror symmetry, a conjecture is
formulated describing how the diffeomorphism group of a Calabi-Yau manifold Y
should act by families of Fourier-Mukai transforms over the complex moduli
space of the mirror X. The conjecture generalizes a proposal of Kontsevich
relating monodromy transformations and self-equivalences. Supporting evidence
is given in the case of elliptic curves, lattice-polarized K3 surfaces and
Calabi-Yau threefolds. A relation to the global Torelli problem is discussed.Comment: Approx. 20 pages LaTeX. One reference adde
Higher Spin Gravitational Couplings and the Yang--Mills Detour Complex
Gravitational interactions of higher spin fields are generically plagued by
inconsistencies. We present a simple framework that couples higher spins to a
broad class of gravitational backgrounds (including Ricci flat and Einstein)
consistently at the classical level. The model is the simplest example of a
Yang--Mills detour complex, which recently has been applied in the mathematical
setting of conformal geometry. An analysis of asymptotic scattering states
about the trivial field theory vacuum in the simplest version of the theory
yields a rich spectrum marred by negative norm excitations. The result is a
theory of a physical massless graviton, scalar field, and massive vector along
with a degenerate pair of zero norm photon excitations. Coherent states of the
unstable sector of the model do have positive norms, but their evolution is no
longer unitary and their amplitudes grow with time. The model is of
considerable interest for braneworld scenarios and ghost condensation models,
and invariant theory.Comment: 19 pages LaTe
Khovanov homology is an unknot-detector
We prove that a knot is the unknot if and only if its reduced Khovanov
cohomology has rank 1. The proof has two steps. We show first that there is a
spectral sequence beginning with the reduced Khovanov cohomology and abutting
to a knot homology defined using singular instantons. We then show that the
latter homology is isomorphic to the instanton Floer homology of the sutured
knot complement: an invariant that is already known to detect the unknot.Comment: 124 pages, 13 figure
Cognitive Information Processing
Contains reports on three research projects.National Science Foundation (Grant GP-2495)National Institutes of Health (Grant MH-04737-04)National Aeronautics and Space Administration (Grant NsG-496)Joint Services Electronics Program by the U. S. Army Research Office, Durha
Hamiltonian 2-forms in Kahler geometry, III Extremal metrics and stability
This paper concerns the explicit construction of extremal Kaehler metrics on
total spaces of projective bundles, which have been studied in many places. We
present a unified approach, motivated by the theory of hamiltonian 2-forms (as
introduced and studied in previous papers in the series) but this paper is
largely independent of that theory.
We obtain a characterization, on a large family of projective bundles, of
those `admissible' Kaehler classes (i.e., the ones compatible with the bundle
structure in a way we make precise) which contain an extremal Kaehler metric.
In many cases, such as on geometrically ruled surfaces, every Kaehler class is
admissible. In particular, our results complete the classification of extremal
Kaehler metrics on geometrically ruled surfaces, answering several
long-standing questions.
We also find that our characterization agrees with a notion of K-stability
for admissible Kaehler classes. Our examples and nonexistence results therefore
provide a fertile testing ground for the rapidly developing theory of stability
for projective varieties, and we discuss some of the ramifications. In
particular we obtain examples of projective varieties which are destabilized by
a non-algebraic degeneration.Comment: 40 pages, sequel to math.DG/0401320 and math.DG/0202280, but largely
self-contained; partially replaces and extends math.DG/050151
PU(2) monopoles and links of top-level Seiberg-Witten moduli spaces
This is the first of two articles in which we give a proof - for a broad
class of four-manifolds - of Witten's conjecture that the Donaldson and
Seiberg-Witten series coincide, at least through terms of degree less than or
equal to c-2, where c is a linear combination of the Euler characteristic and
signature of the four-manifold. This article is a revision of sections 1-3 of
an earlier version of the article dg-ga/9712005, now split into two parts,
while a revision of sections 4-7 of that earlier version appears in a recently
updated dg-ga/9712005. In the present article, we construct virtual normal
bundles for the Seiberg-Witten strata of the moduli space of PU(2) monopoles
and compute their Chern classes.Comment: Journal fur die Reine und Angewandte Mathematik, to appear; 64 page
Prevalence of chronic pain in the UK : a systematic review and meta-analysis of population studies
Acknowledgements The authors are grateful for the input of Professor Blair Smith (University of Dundee): his counsel early in the project, and his advice and comments regarding the search strategy; and Professor Danielle van der Windt (Keele University) for helpful advice and comments. Funding The British Pain Society provided financial assistance to AF with the costs of this project. PC was partly supported by an Arthritis Research UK Primary Care Centre grant (reference: 18139).Peer reviewedPublisher PD
Let's Twist Again: N=2 Super Yang Mills Theory Coupled To Matter
We give the twisted version of N=2 Super Yang Mills theory coupled to matter,
including quantum fields, supersymmetry transformations, action and algebraic
structure. We show that the whole action, coupled to matter, can be written as
the variation of a nilpotent operator, modulo field equations. An extended
Slavnov-Taylor identity, collecting gauge symmetry and supersymmetry, is
written, which allows to define the web of algebraic constraints, in view of
the algebraic renormalization and of the extension of the non-renormalization
theorems holding for N=2 SYM theory without matter.Comment: 28 pages, final version to be published on CQ
PU(2) monopoles. II: Top-level Seiberg-Witten moduli spaces and Witten's conjecture in low degrees
In this article we complete the proof---for a broad class of
four-manifolds---of Witten's conjecture that the Donaldson and Seiberg-Witten
series coincide, at least through terms of degree less than or equal to c-2,
where c is a linear combination of the Euler characteristic and signature of
the four-manifold. This article is a revision of sections 4--7 of an earlier
version, while a revision of sections 1--3 of that earlier version now appear
in a separate companion article (math.DG/0007190). Here, we use our
computations of Chern classes for the virtual normal bundles for the
Seiberg-Witten strata from the companion article (math.DG/0007190), a
comparison of all the orientations, and the PU(2) monopole cobordism to compute
pairings with the links of level-zero Seiberg-Witten moduli subspaces of the
moduli space of PU(2) monopoles. These calculations then allow us to compute
low-degree Donaldson invariants in terms of Seiberg-Witten invariants and
provide a partial verification of Witten's conjecture.Comment: Journal fur die Reine und Angewandte Mathematik, to appear; 65 pages.
Revision of sections 4-7 of version v1 (December 1997
Permeation of CO2 and N2 through glassy poly(dimethyl phenylene) oxide under steady- and presteady-state conditions
Glassy polymers are often used for gas separations because of their high selectivity. Although the dual-mode permeation model correctly fits their sorption and permeation isotherms, its physical interpretation is disputed, and it does not describe permeation far from steady state, a condition expected when separations involve intermittent renewable energy sources. To develop a more comprehensive permeation model, we combine experiment, molecular dynamics, and multiscale reactionâdiffusion modeling to characterize the time-dependent permeation of N2 and CO2 through a glassy poly(dimethyl phenylene oxide) membrane, a model system. Simulations of experimental time-dependent permeation data for both gases in the presteady-state and steady-state regimes show that both single- and dual-mode reactionâdiffusion models reproduce the experimental observations, and that sorbed gas concentrations lag the external pressure rise. The results point to environment-sensitive diffusion coefficients as a vital characteristic of transport in glassy polymers
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