165 research outputs found
Deformations of calibrated subbundles of Euclidean spaces via twisting by special sections
We extend the "bundle constructions" of calibrated submanifolds, due to
Harvey--Lawson in the special Lagrangian case, and to
Ionel--Karigiannis--Min-Oo in the cases of exceptional calibrations, by
"twisting" the bundles by a special (harmonic, holomorphic, parallel) section
of a complementary bundle. The existence of such deformations shows that the
moduli space of calibrated deformations of these "calibrated subbundles"
includes deformations which destroy the linear structure of the fibre.Comment: 16 pages, no figures. Version 2: Only minor cosmetic and
typographical revisions. To appear in "Annals of Global Analysis and
Geometry.
Book Reviews
Reviews of the following books: A Brides Passage: Susan Hathorns Year Under Sail edited by Catherine Petroski; Inventing Acadia: Artists and Tourists at Mount Desert by Pamela J. Belanger; Migration and the Origins of the English Atlantic World by Alison Games; Johnson\u27s Kingdom: The Story of a Nineteenth Century Industrial Kingdom in the Town of Wayne, Maine by Edward Kallop; Saltwater Foodways: New Englanders and Their Food, at Sea and Ashore in the Nineteenth Century By Sandra L. Olive
Type IIA Orientifold Limit of M-Theory on Compact Joyce 8-Manifold of Spin(7)-Holonomy
We show that M-theory compactified on a compact Joyce 8-manifold of
-holonomy, which yields an effective theory in with = 1
supersymmetry, admits at some special points in it moduli space a description
in terms of type IIA theory on an orientifold of compact Joyce 7-manifold of
-holonomy. We find the evidence in favour of this duality by computing the
massless spectra on both M-thory side and type IIA side. For the latter, we
compute the massless spectra by going to the orbifold limit of the Joyce
7-manifold.Comment: 26 pages, 2 eps figures, Latex file, two references and one footnote
added, corrected some typo
Asymptotically cylindrical 7-manifolds of holonomy G_2 with applications to compact irreducible G_2-manifolds
We construct examples of exponentially asymptotically cylindrical Riemannian
7-manifolds with holonomy group equal to G_2. To our knowledge, these are the
first such examples. We also obtain exponentially asymptotically cylindrical
coassociative calibrated submanifolds. Finally, we apply our results to show
that one of the compact G_2-manifolds constructed by Joyce by desingularisation
of a flat orbifold T^7/\Gamma can be deformed to one of the compact
G_2-manifolds obtainable as a generalized connected sum of two exponentially
asymptotically cylindrical SU(3)-manifolds via the method given by the first
author (math.DG/0012189).Comment: 36 pages; v2: corrected trivial typos; v3: some arguments corrected
and improved; v4: a number of improvements on presentation, paritularly in
sections 4 and 6, including an added picture
Super Calabi-Yau's and Special Lagrangians
We apply mirror symmetry to the super Calabi-Yau manifold CP^{(n|n+1)} and
show that the mirror can be recast in a form which depends only on the
superdimension and which is reminiscent of a generalized conifold. We discuss
its geometrical properties in comparison to the familiar conifold geometry. In
the second part of the paper examples of special-Lagrangian submanifolds are
constructed for a class of super Calabi-Yau's. We finally comment on their
infinitesimal deformations.Comment: 20 pages, no figures, latex; v2: references added; v3: minor
clarifications added, version published in JHE
Chirality Change in String Theory
It is known that string theory compactifications leading to low energy
effective theories with different chiral matter content ({\it e.g.} different
numbers of standard model generations) are connected through phase transitions,
described by non-trivial quantum fixed point theories.
We point out that such compactifications are also connected on a purely
classical level, through transitions that can be described using standard
effective field theory. We illustrate this with examples, including some in
which the transition proceeds entirely through supersymmetric configurations.Comment: 50 pages, 2 figure
Effective Electromagnetic Lagrangian at Finite Temperature and Density in the Electroweak Model
Using the exact propagators in a constant magnetic field, the effective
electromagnetic Lagrangian at finite temperature and density is calculated to
all orders in the field strength B within the framework of the complete
electroweak model, in the weak coupling limit. The partition function and free
energy are obtained explicitly and the finite temperature effective coupling is
derived in closed form. Some implications of this result, potentially
interesting to astrophysics and cosmology, are discussed.Comment: 14 pages, Revtex
Deformations of calibrated D-branes in flux generalized complex manifolds
We study massless deformations of generalized calibrated cycles, which
describe, in the language of generalized complex geometry, supersymmetric
D-branes in N=1 supersymmetric compactifications with fluxes. We find that the
deformations are classified by the first cohomology group of a Lie algebroid
canonically associated to the generalized calibrated cycle, seen as a
generalized complex submanifold with respect to the integrable generalized
complex structure of the bulk. We provide examples in the SU(3) structure case
and in a `genuine' generalized complex structure case. We discuss cases of
lifting of massless modes due to world-volume fluxes, background fluxes and a
generalized complex structure that changes type.Comment: 52 pages, added references, added comment on ellipticity in appendix
B, made minor changes according to instructions referee JHE
Branes on Generalized Calibrated Submanifolds
We extend previous results on generalized calibrations to describe
supersymmetric branes in supergravity backgrounds with diverse fields turned
on, and provide several new classes of examples. As an important application,
we show that supersymmetric D-branes in compactifications with field strength
fluxes, and on SU(3)-structure spaces, wrap generalized calibrated
submanifolds, defined by simple conditions in terms of the underlying globally
defined, but non-closed, 2- and 3-forms. We provide examples where the
geometric moduli of D-branes (for instance D7-branes in 3-form flux
configurations) are lifted by the generalized calibration condition. In
addition, we describe supersymmetric D6-branes on generalized calibrated
3-submanifolds of half-flat manifolds, which provide the mirror of B-type
D-branes in IIB CY compactifications with 3-form fluxes. Supersymmetric sets of
such D-branes carrying no homology charges are mirror to supersymmetric sets of
D-branes which are homologically non-trivial, but trivial in K-theory. As an
additional application, we describe models with chiral gauge sectors, realized
in terms of generalized calibrated brane box configurations of NS- and
D5-branes, which are supersymmetric but carry no charges, so that no
orientifold planes are required in the compactification.Comment: 40 pages, 3 figures, references adde
Yukawa couplings in intersecting D-brane models
We compute the Yukawa couplings among chiral fields in toroidal Type II
compactifications with wrapping D6-branes intersecting at angles. Those models
can yield realistic standard model spectrum living at the intersections. The
Yukawa couplings depend both on the Kahler and open string moduli but not on
the complex structure. They arise from worldsheet instanton corrections and are
found to be given by products of complex Jacobi theta functions with
characteristics. The Yukawa couplings for a particular intersecting brane
configuration yielding the chiral spectrum of the MSSM are computed as an
example. We also show how our methods can be extended to compute Yukawa
couplings on certain classes of elliptically fibered CY manifolds which are
mirror to complex cones over del Pezzo surfaces. We find that the Yukawa
couplings in intersecting D6-brane models have a mathematical interpretation in
the context of homological mirror symmetry. In particular, the computation of
such Yukawa couplings is related to the construction of Fukaya's category in a
generic symplectic manifold.Comment: 47 pages, using JHEP3.cls, 11 figures. Typos and other minor
corrections. References adde
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