158 research outputs found
A G_2 Unification of the Deformed and Resolved Conifolds
We find general first-order equations for G_2 metrics of cohomogeneity one
with S^3\times S^3 principal orbits. These reduce in two special cases to
previously-known systems of first-order equations that describe regular
asymptotically locally conical (ALC) metrics \bB_7 and \bD_7, which have
weak-coupling limits that are S^1 times the deformed conifold and the resolved
conifold respectively. Our more general first-order equations provide a
supersymmetric unification of the two Calabi-Yau manifolds, since the metrics
\bB_7 and \bD_7 arise as solutions of the {\it same} system of first-order
equations, with different values of certain integration constants.
Additionally, we find a new class of ALC G_2 solutions to these first-order
equations, which we denote by \wtd\bC_7, whose topology is an \R^2 bundle over
T^{1,1}. There are two non-trivial parameters characterising the homogeneous
squashing of the T^{1,1} bolt. Like the previous examples of the \bB_7 and
\bD_7 ALC metrics, here too there is a U(1) isometry for which the circle has
everywhere finite and non-zero length. The weak-coupling limit of the \wtd\bC_7
metrics gives S^1 times a family of Calabi-Yau metrics on a complex line bundle
over S^2\times S^2, with an adjustable parameter characterising the relative
sizes of the two S^2 factors.Comment: Latex, 14 pages, Major simplification of first-order equations;
references amende
On the geometry of closed G2-structure
We give an answer to a question posed recently by R.Bryant, namely we show
that a compact 7-dimensional manifold equipped with a G2-structure with closed
fundamental form is Einstein if and only if the Riemannian holonomy of the
induced metric is contained in G2. This could be considered to be a G2 analogue
of the Goldberg conjecture in almost Kahler geometry. The result was
generalized by R.L.Bryant to closed G2-structures with too tightly pinched
Ricci tensor. We extend it in another direction proving that a compact
G2-manifold with closed fundamental form and divergence-free Weyl tensor is a
G2-manifold with parallel fundamental form. We introduce a second symmetric
Ricci-type tensor and show that Einstein conditions applied to the two Ricci
tensors on a closed G2-structure again imply that the induced metric has
holonomy group contained in G2.Comment: 14 pages, the Einstein condition in the assumptions of the Main
theorem is generalized to the assumption that the Weyl tensor is
divergence-free, clarity improved, typos correcte
Supersymmetric M3-branes and G_2 Manifolds
We obtain a generalisation of the original complete Ricci-flat metric of G_2
holonomy on R^4\times S^3 to a family with a non-trivial parameter \lambda. For
generic \lambda the solution is singular, but it is regular when
\lambda={-1,0,+1}. The case \lambda=0 corresponds to the original G_2 metric,
and \lambda ={-1,1} are related to this by an S_3 automorphism of the SU(2)^3
isometry group that acts on the S^3\times S^3 principal orbits. We then
construct explicit supersymmetric M3-brane solutions in D=11 supergravity,
where the transverse space is a deformation of this class of G_2 metrics. These
are solutions of a system of first-order differential equations coming from a
superpotential. We also find M3-branes in the deformed backgrounds of new
G_2-holonomy metrics that include one found by A. Brandhuber, J. Gomis, S.
Gubser and S. Gukov, and show that they also are supersymmetric.Comment: Latex, 29 pages. This corrects a previous version in which it was
claimed that the M3-brane solutions were pseudo-supersymmetric rather than
supersymmetri
Electron-Hole Correlations and Optical Excitonic Gaps in Quantum-Dot Quantum Wells: Tight-Binding Approach
Electron-hole correlation in quantum-dot quantum wells (QDQW's) is
investigated by incorporating Coulomb and exchange interactions into an
empirical tight-binding model. Sufficient electron and hole single-particle
states close to the band edge are included in the configuration to achieve
convergence of the first spin-singlet and triplet excitonic energies within a
few meV. Coulomb shifts of about 100 meV and exchange splittings of about 1 meV
are found for CdS/HgS/CdS QDQW's (4.7 nm CdS core diameter, 0.3 nm HgS well
width and 0.3 nm to 1.5 nm CdS clad thickness) which have been characterized
experimentally by Weller and co-workers [ D. Schooss, A. Mews, A. Eychmuller,
H. Weller, Phys. Rev. B, 49, 17072 (1994)]. The optical excitonic gaps
calculated for those QDQW's are in good agreement with the experiment.Comment: 3 figures, to appear in Phys.Rev.
New Complete Non-compact Spin(7) Manifolds
We construct new explicit metrics on complete non-compact Riemannian
8-manifolds with holonomy Spin(7). One manifold, which we denote by A_8, is
topologically R^8 and another, which we denote by B_8, is the bundle of chiral
spinors over . Unlike the previously-known complete non-compact metric of
Spin(7) holonomy, which was also defined on the bundle of chiral spinors over
S^4, our new metrics are asymptotically locally conical (ALC): near infinity
they approach a circle bundle with fibres of constant length over a cone whose
base is the squashed Einstein metric on CP^3. We construct the
covariantly-constant spinor and calibrating 4-form. We also obtain an
L^2-normalisable harmonic 4-form for the A_8 manifold, and two such 4-forms (of
opposite dualities) for the B_8 manifold. We use the metrics to construct new
supersymmetric brane solutions in M-theory and string theory. In particular, we
construct resolved fractional M2-branes involving the use of the L^2 harmonic
4-forms, and show that for each manifold there is a supersymmetric example. An
intriguing feature of the new A_8 and B_8 Spin(7) metrics is that they are
actually the same local solution, with the two different complete manifolds
corresponding to taking the radial coordinate to be either positive or
negative. We make a comparison with the Taub-NUT and Taub-BOLT metrics, which
by contrast do not have special holonomy. In an appendix we construct the
general solution of our first-order equations for Spin(7) holonomy, and obtain
further regular metrics that are complete on manifolds B^+_8 and B^-_8 similar
to B_8.Comment: Latex, 29 pages. Appendix obtaining general solution of first-order
equations and additional complete Spin(7) manifolds adde
Intersecting 6-branes from new 7-manifolds with G_2 holonomy
We discuss a new family of metrics of 7-manifolds with G_2 holonomy, which
are R^3 bundles over a quaternionic space. The metrics depend on five
parameters and have two Abelian isometries. Certain singularities of the G_2
manifolds are related to fixed points of these isometries; there are two
combinations of Killing vectors that possess co-dimension four fixed points
which yield upon compactification only intersecting D6-branes if one also
identifies two parameters. Two of the remaining parameters are quantized and we
argue that they are related to the number of D6-branes, which appear in three
stacks. We perform explicitly the reduction to the type IIA model.Comment: 25 pages, 1 figure, Latex, small changes and add refs, version
appeared in JHE
String and M-theory Deformations of Manifolds with Special Holonomy
The R^4-type corrections to ten and eleven dimensional supergravity required
by string and M-theory imply corrections to supersymmetric supergravity
compactifications on manifolds of special holonomy, which deform the metric
away from the original holonomy. Nevertheless, in many such cases, including
Calabi-Yau compactifications of string theory and G_2-compactifications of
M-theory, it has been shown that the deformation preserves supersymmetry
because of associated corrections to the supersymmetry transformation rules,
Here, we consider Spin(7) compactifications in string theory and M-theory, and
a class of non-compact SU(5) backgrounds in M-theory. Supersymmetry survives in
all these cases too, despite the fact that the original special holonomy is
perturbed into general holonomy in each case.Comment: Improved discussion of SU(5) holonomy backgrounds. Other minor typos
corrected. Latex with JHEP3.cls, 42 page
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
General Metrics of G_2 Holonomy and Contraction Limits
We obtain first-order equations for G_2 holonomy of a wide class of metrics
with S^3\times S^3 principal orbits and SU(2)\times SU(2) isometry, using a
method recently introduced by Hitchin. The new construction extends previous
results, and encompasses all previously-obtained first-order systems for such
metrics. We also study various group contractions of the principal orbits,
focusing on cases where one of the S^3 factors is subjected to an Abelian,
Heisenberg or Euclidean-group contraction. In the Abelian contraction, we
recover some recently-constructed G_2 metrics with S^3\times T^3 principal
orbits. We obtain explicit solutions of these contracted equations in cases
where there is an additional U(1) isometry. We also demonstrate that the only
solutions of the full system with S^3\times T^3 principal orbits that are
complete and non-singular are either flat R^4 times T^3, or else the direct
product of Eguchi-Hanson and T^3, which is asymptotic to R^4/Z_2\times T^3.
These examples are in accord with a general discussion of isometric fibrations
by tori which, as we show, in general split off as direct products. We also
give some (incomplete) examples of fibrations of G_2 manifolds by associative
3-tori with either T^4 or K3 as base.Comment: Latex, 27 page
Orientifolds and Slumps in G_2 and Spin(7) Metrics
We discuss some new metrics of special holonomy, and their roles in string
theory and M-theory. First we consider Spin(7) metrics denoted by C_8, which
are complete on a complex line bundle over CP^3. The principal orbits are S^7,
described as a triaxially squashed S^3 bundle over S^4. The behaviour in the
S^3 directions is similar to that in the Atiyah-Hitchin metric, and we show how
this leads to an M-theory interpretation with orientifold D6-branes wrapped
over S^4. We then consider new G_2 metrics which we denote by C_7, which are
complete on an R^2 bundle over T^{1,1}, with principal orbits that are
S^3\times S^3. We study the C_7 metrics using numerical methods, and we find
that they have the remarkable property of admitting a U(1) Killing vector whose
length is nowhere zero or infinite. This allows one to make an everywhere
non-singular reduction of an M-theory solution to give a solution of the type
IIA theory. The solution has two non-trivial S^2 cycles, and both carry
magnetic charge with respect to the R-R vector field. We also discuss some
four-dimensional hyper-Kahler metrics described recently by Cherkis and
Kapustin, following earlier work by Kronheimer. We show that in certain cases
these metrics, whose explicit form is known only asymptotically, can be related
to metrics characterised by solutions of the su(\infty) Toda equation, which
can provide a way of studying their interior structure.Comment: Latex, 45 pages; minor correction
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