168 research outputs found
Minimal cubic cones via Clifford algebras
We construct two infinite families of algebraic minimal cones in . The
first family consists of minimal cubics given explicitly in terms of the
Clifford systems. We show that the classes of congruent minimal cubics are in
one to one correspondence with those of geometrically equivalent Clifford
systems. As a byproduct, we prove that for any , , there is
at least one minimal cone in given by an irreducible homogeneous cubic
polynomial. The second family consists of minimal cones in , ,
defined by an irreducible homogeneous polynomial of degree . These examples
provide particular answers to the questions on algebraic minimal cones posed by
Wu-Yi Hsiang in the 1960's.Comment: Final version, corrects typos in Table
On the geometry of closed G2-structure
We give an answer to a question posed recently by R.Bryant, namely we show
that a compact 7-dimensional manifold equipped with a G2-structure with closed
fundamental form is Einstein if and only if the Riemannian holonomy of the
induced metric is contained in G2. This could be considered to be a G2 analogue
of the Goldberg conjecture in almost Kahler geometry. The result was
generalized by R.L.Bryant to closed G2-structures with too tightly pinched
Ricci tensor. We extend it in another direction proving that a compact
G2-manifold with closed fundamental form and divergence-free Weyl tensor is a
G2-manifold with parallel fundamental form. We introduce a second symmetric
Ricci-type tensor and show that Einstein conditions applied to the two Ricci
tensors on a closed G2-structure again imply that the induced metric has
holonomy group contained in G2.Comment: 14 pages, the Einstein condition in the assumptions of the Main
theorem is generalized to the assumption that the Weyl tensor is
divergence-free, clarity improved, typos correcte
Born-Infeld particles and Dirichlet p-branes
Born-Infeld theory admits finite energy point particle solutions with
-function sources, BIons. I discuss their role in the theory of
Dirichlet -branes as the ends of strings intersecting the brane when the
effects of gravity are ignored. There are also topologically non-trivial
electrically neutral catenoidal solutions looking like two -branes joined by
a throat. The general solution is a non-singular deformation of the catenoid if
the charge is not too large and a singular deformation of the BIon solution for
charges above that limit. The intermediate solution is BPS and Coulomb-like.
Performing a duality rotation we obtain monopole solutions, the BPS limit being
a solution of the abelian Bogolmol'nyi equations. The situation closely
resembles that of sub and super extreme black-brane solutions of the
supergravity theories. I also show that certain special Lagrangian submanifolds
of , , may be regarded as supersymmetric configurations
consisting of -branes at angles joined by throats which are the sources of
global monopoles. Vortex solutions are also exhibited.Comment: 40 pages Latex file, no figure
Seismic Behaviour of the Christchurch Women's Hospital
1-pageThe objective of this project is to collect perishable seismic response data from the baseisolated
Christchurch Women's Hospital. The strong and continuing sequence of aftershocks
presents a unique opportunity to capture high-fidelity data from a modern base-isolated
facility. These measurements will provide quantitative information required to assess the
mechanisms at play in this and in many other seismically-isolated structures
M-theory on eight-manifolds revisited: N=1 supersymmetry and generalized Spin(7) structures
The requirement of supersymmetry for M-theory backgrounds of the
form of a warped product , where is an eight-manifold
and is three-dimensional Minkowski or AdS space, implies the
existence of a nowhere-vanishing Majorana spinor on . lifts to a
nowhere-vanishing spinor on the auxiliary nine-manifold , where
is a circle of constant radius, implying the reduction of the structure
group of to . In general, however, there is no reduction of the
structure group of itself. This situation can be described in the language
of generalized structures, defined in terms of certain spinors of
. We express the condition for supersymmetry
in terms of differential equations for these spinors. In an equivalent
formulation, working locally in the vicinity of any point in in terms of a
`preferred' structure, we show that the requirement of
supersymmetry amounts to solving for the intrinsic torsion and all irreducible
flux components, except for the one lying in the of , in
terms of the warp factor and a one-form on (not necessarily
nowhere-vanishing) constructed as a bilinear; in addition, is
constrained to satisfy a pair of differential equations. The formalism based on
the group is the most suitable language in which to describe
supersymmetric compactifications on eight-manifolds of structure,
and/or small-flux perturbations around supersymmetric compactifications on
manifolds of holonomy.Comment: 24 pages. V2: introduction slightly extended, typos corrected in the
text, references added. V3: the role of Spin(7) clarified, erroneous
statements thereof corrected. New material on generalized Spin(7) structures
in nine dimensions. To appear in JHE
Negative Energy Density in Calabi-Yau Compactifications
We show that a large class of supersymmetric compactifications, including all
simply connected Calabi-Yau and G_2 manifolds, have classical configurations
with negative energy density as seen from four dimensions. In fact, the energy
density can be arbitrarily negative -- it is unbounded from below.
Nevertheless, positive energy theorems show that the total ADM energy remains
positive. Physical consequences of the negative energy density include new
thermal instabilities, and possible violations of cosmic censorship.Comment: 25 pages, v2: few clarifying comments and reference adde
De Sitter and Schwarzschild-De Sitter According to Schwarzschild and De Sitter
When de Sitter first introduced his celebrated spacetime, he claimed,
following Schwarzschild, that its spatial sections have the topology of the
real projective space RP^3 (that is, the topology of the group manifold SO(3))
rather than, as is almost universally assumed today, that of the sphere S^3.
(In modern language, Schwarzschild was disturbed by the non-local correlations
enforced by S^3 geometry.) Thus, what we today call "de Sitter space" would not
have been accepted as such by de Sitter. There is no real basis within
classical cosmology for preferring S^3 to RP^3, but the general feeling appears
to be that the distinction is in any case of little importance. We wish to
argue that, in the light of current concerns about the nature of de Sitter
space, this is a mistake. In particular, we argue that the difference between
"dS(S^3)" and "dS(RP^3)" may be very important in attacking the problem of
understanding horizon entropies. In the approach to de Sitter entropy via
Schwarzschild-de Sitter spacetime, we find that the apparently trivial
difference between RP^3 and S^3 actually leads to very different perspectives
on this major question of quantum cosmology.Comment: 26 pages, 8 figures, typos fixed, references added, equation numbers
finally fixed, JHEP versio
A measurement of the tau mass and the first CPT test with tau leptons
We measure the mass of the tau lepton to be 1775.1+-1.6(stat)+-1.0(syst.) MeV
using tau pairs from Z0 decays. To test CPT invariance we compare the masses of
the positively and negatively charged tau leptons. The relative mass difference
is found to be smaller than 3.0 10^-3 at the 90% confidence level.Comment: 10 pages, 4 figures, Submitted to Phys. Letts.
Measurement of the B0 Lifetime and Oscillation Frequency using B0->D*+l-v decays
The lifetime and oscillation frequency of the B0 meson has been measured
using B0->D*+l-v decays recorded on the Z0 peak with the OPAL detector at LEP.
The D*+ -> D0pi+ decays were reconstructed using an inclusive technique and the
production flavour of the B0 mesons was determined using a combination of tags
from the rest of the event. The results t_B0 = 1.541 +- 0.028 +- 0.023 ps, Dm_d
= 0.497 +- 0.024 +- 0.025 ps-1 were obtained, where in each case the first
error is statistical and the second systematic.Comment: 17 pages, 4 figures, submitted to Phys. Lett.
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