767 research outputs found
Wilson lines and Chern-Simons flux in explicit heterotic Calabi-Yau compactifications
We study to what extent Wilson lines in heterotic Calabi-Yau
compactifications lead to non-trivial H-flux via Chern-Simons terms. Wilson
lines are basic ingredients for Standard Model constructions but their induced
H-flux may affect the consistency of the leading order background geometry and
of the two-dimensional worldsheet theory. Moreover H-flux in heterotic
compactifications would play an important role for moduli stabilization and
could strongly constrain the supersymmetry breaking scale. We show how to
compute H-flux and the corresponding superpotential, given an explicit complete
intersection Calabi-Yau compactification and choice of Wilson lines. We do so
by classifying special Lagrangian submanifolds in the Calabi-Yau, understanding
how the Wilson lines project onto these submanifolds, and computing their
Chern-Simons invariants. We illustrate our procedure with the quintic
hypersurface as well as the split-bicubic, which can provide a potentially
realistic three generation model.Comment: 41 pages, 7 figures. v2: Minor corrections, published versio
Generalized isothermic lattices
We study multidimensional quadrilateral lattices satisfying simultaneously
two integrable constraints: a quadratic constraint and the projective Moutard
constraint. When the lattice is two dimensional and the quadric under
consideration is the Moebius sphere one obtains, after the stereographic
projection, the discrete isothermic surfaces defined by Bobenko and Pinkall by
an algebraic constraint imposed on the (complex) cross-ratio of the circular
lattice. We derive the analogous condition for our generalized isthermic
lattices using Steiner's projective structure of conics and we present basic
geometric constructions which encode integrability of the lattice. In
particular, we introduce the Darboux transformation of the generalized
isothermic lattice and we derive the corresponding Bianchi permutability
principle. Finally, we study two dimensional generalized isothermic lattices,
in particular geometry of their initial boundary value problem.Comment: 19 pages, 11 figures; v2. some typos corrected; v3. new references
added, higlighted similarities and differences with recent papers on the
subjec
On reconstructing n-point configurations from the distribution of distances or areas
One way to characterize configurations of points up to congruence is by
considering the distribution of all mutual distances between points. This paper
deals with the question if point configurations are uniquely determined by this
distribution. After giving some counterexamples, we prove that this is the case
for the vast majority of configurations. In the second part of the paper, the
distribution of areas of sub-triangles is used for characterizing point
configurations. Again it turns out that most configurations are reconstructible
from the distribution of areas, though there are counterexamples.Comment: 21 pages, late
Entanglement of four-qubit systems: a geometric atlas with polynomial compass II (the tame world)
We propose a new approach to the geometry of the four-qubit entanglement
classes depending on parameters. More precisely, we use invariant theory and
algebraic geometry to describe various stratifications of the Hilbert space by
SLOCC invariant algebraic varieties. The normal forms of the four-qubit
classification of Verstraete {\em et al.} are interpreted as dense subsets of
components of the dual variety of the set of separable states and an algorithm
based on the invariants/covariants of the four-qubit quantum states is proposed
to identify a state with a SLOCC equivalent normal form (up to qubits
permutation).Comment: 49 pages, 16 figure
Complex Hyperbolic Cone Structures on the Configuration Spaces
The space of marked n distinct points on the complex
projective line up to projective transformations will be called a
configuration space. There are two families of complex hyperbolic structures on the configuration space constructed by Deligne-
Mostow and by Thurston. We review that these families are the
same, and then exhibit the families for n = 4, 5 in constrast with
the deformation theory of real hyperbolic cone 3-manifolds
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