58,319 research outputs found
NC Calabi-Yau Orbifolds in Toric Varieties with Discrete Torsion
Using the algebraic geometric approach of Berenstein et {\it al}
(hep-th/005087 and hep-th/009209) and methods of toric geometry, we study non
commutative (NC) orbifolds of Calabi-Yau hypersurfaces in toric varieties with
discrete torsion. We first develop a new way of getting complex mirror
Calabi-Yau hypersurfaces in toric manifolds with a action and analyze the general group of the
discrete isometries of . Then we build a general class of
complex dimension NC mirror Calabi-Yau orbifolds where the non
commutativity parameters are solved in terms of discrete
torsion and toric geometry data of in which the original
Calabi-Yau hypersurfaces is embedded. Next we work out a generalization of the
NC algebra for generic dimensions NC Calabi-Yau manifolds and give various
representations depending on different choices of the Calabi-Yau toric geometry
data. We also study fractional D-branes at orbifold points. We refine and
extend the result for NC to higher dimensional torii orbifolds
in terms of Clifford algebra.Comment: 38 pages, Late
Toric Varieties with NC Toric Actions: NC Type IIA Geometry
Extending the usual actions of toric manifolds by
allowing asymmetries between the various factors, we build
a class of non commutative (NC) toric varieties . We
construct NC complex dimension Calabi-Yau manifolds embedded in
by using the algebraic geometry method. Realizations
of NC toric group are given in presence and absence of
quantum symmetries and for both cases of discrete or continuous spectrums. We
also derive the constraint eqs for NC Calabi-Yau backgrounds
embedded in and work out their
solutions. The latters depend on the Calabi-Yau condition , being the charges of % ;
but also on the toric data of the polygons associated to . Moreover,
we study fractional branes at singularities and show that, due to the
complete reducibility property of group representations,
there is an infinite number of fractional branes. We also give the
generalized Berenstein and Leigh quiver diagrams for discrete and continuous
representation spectrums. An illustrating example is
presented.Comment: 25 pages, no figure
Invariant measures on multimode quantum Gaussian states
We derive the invariant measure on the manifold of multimode quantum Gaussian
states, induced by the Haar measure on the group of Gaussian unitary
transformations. To this end, by introducing a bipartition of the system in two
disjoint subsystems, we use a parameterization highlighting the role of
nonlocal degrees of freedom -- the symplectic eigenvalues -- which characterize
quantum entanglement across the given bipartition. A finite measure is then
obtained by imposing a physically motivated energy constraint. By averaging
over the local degrees of freedom we finally derive the invariant distribution
of the symplectic eigenvalues in some cases of particular interest for
applications in quantum optics and quantum information.Comment: 17 pages, comments are welcome. v2: presentation improved and typos
corrected. Close to the published versio
Charge Orbits of Symmetric Special Geometries and Attractors
We study the critical points of the black hole scalar potential in
N=2, d=4 supergravity coupled to vector multiplets, in an
asymptotically flat extremal black hole background described by a
2(n_{V}+1)-dimensional dyonic charge vector and (complex) scalar fields which
are coordinates of a special K\"{a}hler manifold.
For the case of homogeneous symmetric spaces, we find three general classes
of regular attractor solutions with non-vanishing Bekenstein-Hawking entropy.
They correspond to three (inequivalent) classes of orbits of the charge vector,
which is in a 2(n_{V}+1)-dimensional representation of the U-duality
group. Such orbits are non-degenerate, namely they have non-vanishing quartic
invariant (for rank-3 spaces). Other than the 1/2-BPS one, there are two other
distinct non-BPS classes of charge orbits, one of which has vanishing central
charge.
The three species of solutions to the N=2 extremal black hole attractor
equations give rise to different mass spectra of the scalar fluctuations, whose
pattern can be inferred by using invariance properties of the critical points
of and some group theoretical considerations on homogeneous symmetric
special K\"{a}hler geometry.Comment: 63 pages, 9 Tables. v2: typos fixed, Refs. added, accepted for
publication in IJMP
Compact Riemannian 7-manifolds with holonomy G2. I
This is the second of two papers about metrics of holonomy G2 on compact 7-manifolds. In our first paper [15] we established the existence of a family of metrics of holonomy G2 on a single, compact, simply-connected 7-manifold M, using three general results, Theorems A, B and C. Our purpose in this paper is to explore th
Extended Riemannian Geometry II: Local Heterotic Double Field Theory
We continue our exploration of local Double Field Theory (DFT) in terms of
symplectic graded manifolds carrying compatible derivations and study the case
of heterotic DFT. We start by developing in detail the differential graded
manifold that captures heterotic Generalized Geometry which leads to new
observations on the generalized metric and its twists. We then give a
symplectic pre-NQ-manifold that captures the symmetries and the geometry of
local heterotic DFT. We derive a weakened form of the section condition, which
arises algebraically from consistency of the symmetry Lie 2-algebra and its
action on extended tensors. We also give appropriate notions of twists-which
are required for global formulations-and of the torsion and Riemann tensors.
Finally, we show how the observed -corrections are interpreted
naturally in our framework.Comment: v2: 30 pages, few more details added, typos fixed, published versio
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