4 research outputs found
N=1 Special Geometry, Mixed Hodge Variations and Toric Geometry
We study the superpotential of a certain class of N=1 supersymmetric type II
compactifications with fluxes and D-branes. We show that it has an important
two-dimensional meaning in terms of a chiral ring of the topologically twisted
theory on the world-sheet. In the open-closed string B-model, this chiral ring
is isomorphic to a certain relative cohomology group V, which is the
appropriate mathematical concept to deal with both the open and closed string
sectors. The family of mixed Hodge structures on V then implies for the
superpotential to have a certain geometric structure. This structure represents
a holomorphic, N=1 supersymmetric generalization of the well-known N=2 special
geometry. It defines an integrable connection on the topological family of
open-closed B-models, and a set of special coordinates on the space \cal M of
vev's in N=1 chiral multiplets. We show that it can be given a very concrete
and simple realization for linear sigma models, which leads to a powerful and
systematic method for computing the exact non-perturbative N=1 superpotentials
for a broad class of toric D-brane geometries.Comment: 40p, harvmac-
Holomorphic N=1 Special Geometry of Open--Closed Type II Strings
We outline a general geometric structure that underlies the N=1
superpotentials of a certain class of flux and brane configurations in type II
string compactifications on Calabi-Yau threefolds. This ``holomorphic N=1
special geometry'' is in many respects comparable to, and in a sense an
extension of, the familiar special geometry in N=2 supersymmetric type II
string compactifications. It puts the computation of the instanton-corrected
superpotential W of the four-dimensional N=1 string effective action on a very
similar footing as the familiar computation of the N=2 prepotential F via
mirror symmetry. In this note we present some of the main ideas and results,
while more details as well as some explicit computations will appear in a
companion paperComment: 18 pages, harvmac (b), no figure
A Note on Computations of D-brane Superpotential
We develop some computational methods for the integrals over the 3-chains on
the compact Calabi-Yau 3-folds that plays a prominent role in the analysis of
the topological B-model in the context of the open mirror symmetry. We discuss
such 3-chain integrals in two approaches. In the first approach, we provide a
systematic algorithm to obtain the inhomogeneous Picard-Fuchs equations. In the
second approach, we discuss the analytic continuation of the period integral to
compute the 3-chain integral directly. The latter direct integration method is
applicable for both on-shell and off-shell formalisms.Comment: 61 pages, 5 figures; v2: typos corrected, minor changes, references
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Intersecting Brane Worlds -- A Path to the Standard Model ?
In this review we describe the general geometrical framework of brane world
constructions in orientifolds of type IIA string theory with D6-branes wrapping
3-cycles in a Calabi-Yau 3-fold. These branes generically intersect in points
on the internal space, and the patterns of intersections govern the chiral
fermion spectra. We discuss how the open string spectra in intersecting brane
models are constructed, how the Standard Model can be embedded, and also how
supersymmetry can be realized in this class of string vacua. After the general
considerations we specialize the discussion to the case of orbifold backgrounds
with intersecting D6-branes and to the quintic Calabi-Yau manifold. Then, we
discuss parts of the effective action of intersecting brane world models.
Specifically we compute from the Born-Infeld action of the wrapped D-branes the
tree-level, D-term scalar potential, which is important for the stability of
the considered backgrounds as well as for questions related to supersymmetry
breaking. Second, we review the recent computation concerning of gauge coupling
unification and also of one-loop gauge threshold corrections in intersecting
brane world models. Finally we also discuss some aspects of proton decay in
intersecting brane world models.Comment: 31 pages, To appear in the proceedings of the RTN-workshop ``The
quantum structure of spacetime and the geometric nature of fundamental
interactions'', September 2003 in Copenhagen, revised version contains new
refs and one corrected equatio