472 research outputs found
On the Heterotic World-sheet Instanton Superpotential and its individual Contributions
For supersymmetric heterotic string compactifications on a Calabi-Yau
threefold endowed with a vector bundle the world-sheet superpotential
is a sum of contributions from isolated rational curves \C in ; the
individual contribution is given by an exponential in the K\"ahler class of the
curve times a prefactor given essentially by the Pfaffian which depends on the
moduli of and the complex structure moduli of . Solutions of (or
even of ) can arise either by nontrivial cancellations between the
individual terms in the summation over all contributing curves or because each
of these terms is zero already individually. Concerning the latter case
conditions on the moduli making a single Pfaffian vanish (for special moduli
values) have been investigated. However, even if corresponding moduli -
fulfilling these constraints - for the individual contribution of one curve are
known it is not at all clear whether {\em one} choice of moduli exists which
fulfills the corresponding constraints {\em for all contributing curves
simultaneously}. Clearly this will in general happen only if the conditions on
the 'individual zeroes' had already a conceptual origin which allows them to
fit together consistently. We show that this happens for a class of cases. In
the special case of spectral cover bundles we show that a relevant solution set
has an interesting location in moduli space and is related to transitions which
change the generation number.Comment: 47 page
Perspectives on Pfaffians of Heterotic World-sheet Instantons
To fix the bundle moduli of a heterotic compactification one has to
understand the Pfaffian one-loop prefactor of the classical instanton
contribution. For compactifications on elliptically fibered Calabi-Yau spaces X
this can be made explicit for spectral bundles and world-sheet instantons
supported on rational base curves b: one can express the Pfaffian in a closed
algebraic form as a polynomial, or it may be understood as a theta-function
expression. We elucidate the connection between these two points of view via
the respective perception of the relevant spectral curve, related to its
extrinsic geometry in the ambient space (the elliptic surface in X over b) or
to its intrinsic geometry as abstract Riemann surface. We identify, within a
conceptual description, general vanishing loci of the Pfaffian, and derive
bounds on the vanishing order, relevant to solutions of W=dW=0.Comment: 40 pages; minor changes, discussion section 1.1 adde
A Class of N=1 Dual String Pairs and its Modular Superpotential
We compare the N=1 F-theory compactification of Donagi, Grassi and Witten
with modular superpotential - and some closely related models - to dual
heterotic models. We read of the F-theory spectrum from the cohomology of the
fourfold and discuss on the heterotic side the gauge bundle moduli sector
(including the spectral surface) and the necessary fivebranes. Then we consider
the N=1 superpotential and show how a heterotic superpotential matching the
F-theory computation is built up by worldsheet instantons. Finally we discuss
how the original modular superpotential should be corrected by an additional
modular correction factor, which on the F-theory side matches nicely with a
`curve counting function' for the del Pezzo surface. On the heterotic side we
derive the same factor demanding correct T-duality transformation properties of
the superpotential.Comment: 18 pages, Late
Redundancy reduction in 3D facial motion capture data for animation
Research on the perception of dynamic faces often requires real-time animations with low latency. With an adaptation of principal feature analysis [Cohen et al. 2002], we can reduce the number of facial motion capture markers by 50, while retaining the overall animation quality
Superpotentials for M-theory on a G_2 holonomy manifold and Triality symmetry
For -theory on the holonomy manifold given by the cone on {\bf
S^3}\x {\bf S^3} we consider the superpotential generated by membrane
instantons and study its transformations properties, especially under monodromy
transformations and triality symmetry. We find that the latter symmetry is,
essentially, even a symmetry of the superpotential. As in Seiberg/Witten
theory, where a flat bundle given by the periods of an universal elliptic curve
over the -plane occurs, here a flat bundle related to the Heisenberg group
appears and the relevant universal object over the moduli space is related to
hyperbolic geometry.Comment: 58 pages, latex; references adde
Constraining the Kahler Moduli in the Heterotic Standard Model
Phenomenological implications of the volume of the Calabi-Yau threefolds on
the hidden and observable M-theory boundaries, together with slope stability of
their corresponding vector bundles, constrain the set of Kaehler moduli which
give rise to realistic compactifications of the strongly coupled heterotic
string. When vector bundles are constructed using extensions, we provide simple
rules to determine lower and upper bounds to the region of the Kaehler moduli
space where such compactifications can exist. We show how small these regions
can be, working out in full detail the case of the recently proposed Heterotic
Standard Model. More explicitely, we exhibit Kaehler classes in these regions
for which the visible vector bundle is stable. On the other hand, there is no
polarization for which the hidden bundle is stable.Comment: 28 pages, harvmac. Exposition improved, references and one figure
added, minor correction
Medial Features for Superpixel Segmentation
Image segmentation plays an important role in computer vision and human scene perception. Image oversegmentation is a common technique to overcome the problem of managing the high number of pixels and the reasoning among them. Specifically, a local and coherent cluster that contains a statistically homogeneous region is denoted as a superpixel. In this paper we propose a novel algorithm that segments an image into superpixels employing a new kind of shape centered feature which serve as a seed points for image segmentation, based on Gradient Vector Flow fields (GVF) [14]. The features are located at image locations with salient symmetry. We compare our algorithm to state-of-the-art superpixel algorithms and demonstrate a performance increase on the standard Berkeley Segmentation Dataset
Fluxes in M-theory on 7-manifolds and G structures
We consider warp compactifications of M-theory on 7-manifolds in the presence
of 4-form fluxes and investigate the constraints imposed by supersymmetry. As
long as the 7-manifold supports only one Killing spinor we infer from the
Killing spinor equations that non-trivial 4-form fluxes will necessarily curve
the external 4-dimensional space. On the other hand, if the 7-manifold has at
least two Killing spinors, there is a non-trivial Killing vector yielding a
reduction of the 7-manifold to a 6-manifold and we confirm that 4-form fluxes
can be incorporated if one includes non-trivial SU(3) structures.Comment: 13 pages, Latex; minor changes & add reference
G_2 Domain Walls in M-theory
M-theory is considered in its low-energy limit on a G_2 manifold with
non-vanishing flux. Using the Killing spinor equations for linear flux, an
explicit set of first-order bosonic equations for supersymmetric solutions is
found. These solutions describe a warped product of a domain wall in
four-dimensional space-time and a deformed G_2 manifold. It is shown how these
domain walls arise from the perspective of the associated four-dimensional N=1
effective supergravity theories. We also discuss the inclusion of membrane and
M5-brane sources.Comment: 30 pages, Late
Type IIB Theory on Half-flat Manifolds
In this note we derive the low-energy effective action of type IIB theory
compactified on half-flat manifolds and we show that this precisely coincides
with the low-energy effective action of type IIA theory compactified on a
Calabi-Yau manifold in the presence of NS three-form fluxes. We provide in this
way a further check of the recently formulated conjecture that half-flat
manifolds appear as mirror partners of Calabi-Yau manifolds when NS fluxes are
turned on.Comment: 15 pages, no figure
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