922 research outputs found
On transparent embeddings of point-line geometries
We introduce the class of transparent embeddings for a point-line geometry
as the class of full projective
embeddings of such that the preimage of any projective
line fully contained in is a line of . We
will then investigate the transparency of Pl\"ucker embeddings of projective
and polar grassmannians and spin embeddings of half-spin geometries and dual
polar spaces of orthogonal type. As an application of our results on
transparency, we will derive several Chow-like theorems for polar grassmannians
and half-spin geometries.Comment: 28 Pages/revised version after revie
Grassmann embeddings of polar Grassmannians
In this paper we compute the dimension of the Grassmann embeddings of the
polar Grassmannians associated to a possibly degenerate Hermitian, alternating
or quadratic form with possibly non-maximal Witt index. Moreover, in the
characteristic case, when the form is quadratic and non-degenerate with
bilinearization of minimal Witt index, we define a generalization of the
so-called Weyl embedding (see [I. Cardinali and A. Pasini, Grassmann and Weyl
embeddings of orthogonal Grassmannians. J. Algebr. Combin. 38 (2013), 863-888])
and prove that the Grassmann embedding is a quotient of this generalized
"Weyl-like" embedding. We also estimate the dimension of the latter.Comment: 25 pages/revised version after revie
Supersymmetric D3/D7 for holographic flavors on curved space
We derive a new class of supersymmetric D3/D7 brane configurations, which
allow to holographically describe N=4 SYM coupled to massive N=2 flavor degrees
of freedom on spaces of constant curvature. We systematically solve the
-symmetry condition for D7-brane embeddings into AdS-sliced
AdSS, and find supersymmetric embeddings in a simple closed form.
Up to a critical mass, these embeddings come in surprisingly diverse families,
and we present a first study of their (holographic) phenomenology. We carry out
the holographic renormalization, compute the one-point functions and attempt a
field-theoretic interpretation of the different families. To complete the
catalog of supersymmetric D3/D7 configurations, we construct analogous
embeddings for flavored N=4 SYM on S and dS.Comment: 37 pages, 9 figure
Geometry of Schroedinger Space-Times II: Particle and Field Probes of the Causal Structure
We continue our study of the global properties of the z=2 Schroedinger
space-time. In particular, we provide a codimension 2 isometric embedding which
naturally gives rise to the previously introduced global coordinates.
Furthermore, we study the causal structure by probing the space-time with point
particles as well as with scalar fields. We show that, even though there is no
global time function in the technical sense (Schroedinger space-time being
non-distinguishing), the time coordinate of the global Schroedinger coordinate
system is, in a precise way, the closest one can get to having such a time
function. In spite of this and the corresponding strongly Galilean and almost
pathological causal structure of this space-time, it is nevertheless possible
to define a Hilbert space of normalisable scalar modes with a well-defined
time-evolution. We also discuss how the Galilean causal structure is reflected
and encoded in the scalar Wightman functions and the bulk-to-bulk propagator.Comment: 32 page
Emergent Geometry and Gravity from Matrix Models: an Introduction
A introductory review to emergent noncommutative gravity within Yang-Mills
Matrix models is presented. Space-time is described as a noncommutative brane
solution of the matrix model, i.e. as submanifold of \R^D. Fields and matter on
the brane arise as fluctuations of the bosonic resp. fermionic matrices around
such a background, and couple to an effective metric interpreted in terms of
gravity. Suitable tools are provided for the description of the effective
geometry in the semi-classical limit. The relation to noncommutative gauge
theory and the role of UV/IR mixing is explained. Several types of geometries
are identified, in particular "harmonic" and "Einstein" type of solutions. The
physics of the harmonic branch is discussed in some detail, emphasizing the
non-standard role of vacuum energy. This may provide new approach to some of
the big puzzles in this context. The IKKT model with D=10 and close relatives
are singled out as promising candidates for a quantum theory of fundamental
interactions including gravity.Comment: Invited topical review for Classical and Quantum Gravity. 57 pages, 5
figures. V2,V3: minor corrections and improvements. V4,V5: some improvements,
refs adde
Riemannian Geometry of Noncommutative Surfaces
A Riemannian geometry of noncommutative n-dimensional surfaces is developed
as a first step towards the construction of a consistent noncommutative
gravitational theory. Historically, as well, Riemannian geometry was recognized
to be the underlying structure of Einstein's theory of general relativity and
led to further developments of the latter. The notions of metric and
connections on such noncommutative surfaces are introduced and it is shown that
the connections are metric-compatible, giving rise to the corresponding Riemann
curvature. The latter also satisfies the noncommutative analogue of the first
and second Bianchi identities. As examples, noncommutative analogues of the
sphere, torus and hyperboloid are studied in detail. The problem of covariance
under appropriately defined general coordinate transformations is also
discussed and commented on as compared with other treatments.Comment: 28 pages, some clarifications, examples and references added, version
to appear in J. Math. Phy
Covariant Field Equations, Gauge Fields and Conservation Laws from Yang-Mills Matrix Models
The effective geometry and the gravitational coupling of nonabelian gauge and
scalar fields on generic NC branes in Yang-Mills matrix models is determined.
Covariant field equations are derived from the basic matrix equations of
motions, known as Yang-Mills algebra. Remarkably, the equations of motion for
the Poisson structure and for the nonabelian gauge fields follow from a matrix
Noether theorem, and are therefore protected from quantum corrections. This
provides a transparent derivation and generalization of the effective action
governing the SU(n) gauge fields obtained in [1], including the would-be
topological term. In particular, the IKKT matrix model is capable of describing
4-dimensional NC space-times with a general effective metric. Metric
deformations of flat Moyal-Weyl space are briefly discussed.Comment: 31 pages. V2: minor corrections, references adde
On the Plants Leaves Boundary, "Jupe \`a Godets" and Conformal Embeddings
The stable profile of the boundary of a plant's leaf fluctuating in the
direction transversal to the leaf's surface is described in the framework of a
model called a "surface \`a godets". It is shown that the information on the
profile is encoded in the Jacobian of a conformal mapping (the coefficient of
deformation) corresponding to an isometric embedding of a uniform Cayley tree
into the 3D Euclidean space. The geometric characteristics of the leaf's
boundary (like the perimeter and the height) are calculated. In addition a
symbolic language allowing to investigate statistical properties of a "surface
\`a godets" with annealed random defects of curvature of density is
developed. It is found that at the surface exhibits a phase transition
with critical exponent from the exponentially growing to the flat
structure.Comment: 17 pages (revtex), 8 eps-figures, to appear in Journal of Physics
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