710 research outputs found
Spectral geometry, homogeneous spaces, and differential forms with finite Fourier series
Let G be a compact Lie group acting transitively on Riemannian manifolds M
and N. Let p be a G equivariant Riemannian submersion from M to N. We show that
a smooth differential form on N has finite Fourier series if and only if the
pull back has finite Fourier series on
Noncommutative Geometry Framework and The Feynman's Proof of Maxwell Equations
The main focus of the present work is to study the Feynman's proof of the
Maxwell equations using the NC geometry framework. To accomplish this task, we
consider two kinds of noncommutativity formulations going along the same lines
as Feynman's approach. This allows us to go beyond the standard case and
discover non-trivial results. In fact, while the first formulation gives rise
to the static Maxwell equations, the second formulation is based on the
following assumption
The results extracted from the second formulation are more significant since
they are associated to a non trivial -extension of the Bianchi-set of
Maxwell equations. We find and where
, , and are local functions depending on
the NC -parameter. The novelty of this proof in the NC space is
revealed notably at the level of the corrections brought to the previous
Maxwell equations. These corrections correspond essentially to the possibility
of existence of magnetic charges sources that we can associate to the magnetic
monopole since is not vanishing in general.Comment: LaTeX file, 16 page
Berry effect in acoustical polarization transport in phononic crystals
We derive the semiclassical equations of motion of a transverse acoustical
wave packet propagating in a phononic crystal subject to slowly varying
perturbations. The formalism gives rise to Berry effect terms in the equations
of motion, manifested as the Rytov polarization rotation law and the
polarization-dependent Hall effect. We show that the formalism is also
applicable to the case of non-periodic inhomogeneous media, yielding explicit
expressions for the Berry effect terms.Comment: To appear in JETP Let
Vacuum Spacetimes with Future Trapped Surfaces
In this article we show that one can construct initial data for the Einstein
equations which satisfy the vacuum constraints. This initial data is defined on
a manifold with topology with a regular center and is asymptotically
flat. Further, this initial data will contain an annular region which is
foliated by two-surfaces of topology . These two-surfaces are future
trapped in the language of Penrose. The Penrose singularity theorem guarantees
that the vacuum spacetime which evolves from this initial data is future null
incomplete.Comment: 19 page
M-theory on `toric' G_2 cones and its type II reduction
We analyze a class of conical G_2 metrics admitting two commuting isometries,
together with a certain one-parameter family of G_2 deformations which
preserves these symmetries. Upon using recent results of Calderbank and
Pedersen, we write down the explicit G_2 metric for the most general member of
this family and extract the IIA reduction of M-theory on such backgrounds, as
well as its type IIB dual. By studying the asymptotics of type II fields around
the relevant loci, we confirm the interpretation of such backgrounds in terms
of localized IIA 6-branes and delocalized IIB 5-branes. In particular, we find
explicit, general expressions for the string coupling and R-R/NS-NS forms in
the vicinity of these objects. Our solutions contain and generalize the field
configurations relevant for certain models considered in recent work of Acharya
and Witten.Comment: 45 pages, references adde
Resolutions of C^n/Z_n Orbifolds, their U(1) Bundles, and Applications to String Model Building
We describe blowups of C^n/Z_n orbifolds as complex line bundles over
CP^{n-1}. We construct some gauge bundles on these resolutions. Apart from the
standard embedding, we describe U(1) bundles and an SU(n-1) bundle. Both
blowups and their gauge bundles are given explicitly. We investigate ten
dimensional SO(32) super Yang-Mills theory coupled to supergravity on these
backgrounds. The integrated Bianchi identity implies that there are only a
finite number of U(1) bundle models. We describe how the orbifold gauge shift
vector can be read off from the gauge background. In this way we can assert
that in the blow down limit these models correspond to heterotic C^2/Z_2 and
C^3/Z_3 orbifold models. (Only the Z_3 model with unbroken gauge group SO(32)
cannot be reconstructed in blowup without torsion.) This is confirmed by
computing the charged chiral spectra on the resolutions. The construction of
these blowup models implies that the mismatch between type-I and heterotic
models on T^6/Z_3 does not signal a complication of S-duality, but rather a
problem of type-I model building itself: The standard type-I orbifold model
building only allows for a single model on this orbifold, while the blowup
models give five different models in blow down.Comment: 1+27 pages LaTeX, 2 figures, some typos correcte
A Note on Einstein Sasaki Metrics in D \ge 7
In this paper, we obtain new non-singular Einstein-Sasaki spaces in
dimensions D\ge 7. The local construction involves taking a circle bundle over
a (D-1)-dimensional Einstein-Kahler metric that is itself constructed as a
complex line bundle over a product of Einstein-Kahler spaces. In general the
resulting Einstein-Sasaki spaces are singular, but if parameters in the local
solutions satisfy appropriate rationality conditions, the metrics extend
smoothly onto complete and non-singular compact manifolds.Comment: Latex, 13 page
Cohomogeneity One Manifolds of Spin(7) and G(2) Holonomy
In this paper, we look for metrics of cohomogeneity one in D=8 and D=7
dimensions with Spin(7) and G_2 holonomy respectively. In D=8, we first
consider the case of principal orbits that are S^7, viewed as an S^3 bundle
over S^4 with triaxial squashing of the S^3 fibres. This gives a more general
system of first-order equations for Spin(7) holonomy than has been solved
previously. Using numerical methods, we establish the existence of new
non-singular asymptotically locally conical (ALC) Spin(7) metrics on line
bundles over \CP^3, with a non-trivial parameter that characterises the
homogeneous squashing of CP^3. We then consider the case where the principal
orbits are the Aloff-Wallach spaces N(k,\ell)=SU(3)/U(1), where the integers k
and \ell characterise the embedding of U(1). We find new ALC and AC metrics of
Spin(7) holonomy, as solutions of the first-order equations that we obtained
previously in hep-th/0102185. These include certain explicit ALC metrics for
all N(k,\ell), and numerical and perturbative results for ALC families with AC
limits. We then study D=7 metrics of holonomy, and find new explicit
examples, which, however, are singular, where the principal orbits are the flag
manifold SU(3)/(U(1)\times U(1)). We also obtain numerical results for new
non-singular metrics with principal orbits that are S^3\times S^3. Additional
topics include a detailed and explicit discussion of the Einstein metrics on
N(k,\ell), and an explicit parameterisation of SU(3).Comment: Latex, 60 pages, references added, formulae corrected and additional
discussion on the asymptotic flow of N(k,l) cases adde
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