356 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.
Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds
We present a proof of the mirror conjecture of Aganagic-Vafa
[arXiv:hep-th/0012041] and Aganagic-Klemm-Vafa [arXiv:hep-th/0105045] on disk
enumeration in toric Calabi-Yau 3-folds for all smooth semi-projective toric
Calabi-Yau 3-folds. We consider both inner and outer branes, at arbitrary
framing. In particular, we recover previous results on the conjecture for (i)
an inner brane at zero framing in the total space of the canonical line bundle
of the projective plane (Graber-Zaslow [arXiv:hep-th/0109075]), (ii) an outer
brane at arbitrary framing in the resolved conifold (Zhou [arXiv:1001.0447]),
and (iii) an outer brane at zero framing in the total space of the canonical
line bundle of the projective plane (Brini [arXiv:1102.0281, Section 5.3]).Comment: 39 pages, 11 figure
Calibrated Sub-Bundles in Non-Compact Manifolds of Special Holonomy
This paper is a continuation of math.DG/0408005. We first construct special
Lagrangian submanifolds of the Ricci-flat Stenzel metric (of holonomy SU(n)) on
the cotangent bundle of S^n by looking at the conormal bundle of appropriate
submanifolds of S^n. We find that the condition for the conormal bundle to be
special Lagrangian is the same as that discovered by Harvey-Lawson for
submanifolds in R^n in their pioneering paper. We also construct calibrated
submanifolds in complete metrics with special holonomy G_2 and Spin(7)
discovered by Bryant and Salamon on the total spaces of appropriate bundles
over self-dual Einstein four manifolds. The submanifolds are constructed as
certain subbundles over immersed surfaces. We show that this construction
requires the surface to be minimal in the associative and Cayley cases, and to
be (properly oriented) real isotropic in the coassociative case. We also make
some remarks about using these constructions as a possible local model for the
intersection of compact calibrated submanifolds in a compact manifold with
special holonomy.Comment: 20 pages; for Revised Version: Minor cosmetic changes, some
paragraphs rewritten for improved clarit
Computing top intersections in the tautological ring of
We derive effective recursion formulae of top intersections in the
tautological ring of the moduli space of curves of genus .
As an application, we prove a convolution-type tautological relation in
.Comment: 18 page
Curve counting via stable pairs in the derived category
For a nonsingular projective 3-fold , we define integer invariants
virtually enumerating pairs where is an embedded curve and
is a divisor. A virtual class is constructed on the associated
moduli space by viewing a pair as an object in the derived category of . The
resulting invariants are conjecturally equivalent, after universal
transformations, to both the Gromov-Witten and DT theories of . For
Calabi-Yau 3-folds, the latter equivalence should be viewed as a wall-crossing
formula in the derived category.
Several calculations of the new invariants are carried out. In the Fano case,
the local contributions of nonsingular embedded curves are found. In the local
toric Calabi-Yau case, a completely new form of the topological vertex is
described.
The virtual enumeration of pairs is closely related to the geometry
underlying the BPS state counts of Gopakumar and Vafa. We prove that our
integrality predictions for Gromov-Witten invariants agree with the BPS
integrality. Conversely, the BPS geometry imposes strong conditions on the
enumeration of pairs.Comment: Corrected typos and duality error in Proposition 4.6. 47 page
Macrodimers: ultralong range Rydberg molecules
We study long range interactions between two Rydberg atoms and predict the
existence of ultralong range Rydberg dimers with equilibrium distances of many
thousand Bohr radii. We calculate the dispersion coefficients ,
and for two rubidium atoms in the same excited level , and find
that they scale like , and , respectively. We show that
for certain molecular symmetries, these coefficients lead to long range
potential wells that can support molecular bound levels. Such macrodimers would
be very sensitive to their environment, and could probe weak interactions. We
suggest experiments to detect these macrodimers.Comment: 4 pages, submitted to PR
Scalar ground-state observables in the random phase approximation
We calculate the ground-state expectation value of scalar observables in the
matrix formulation of the random phase approximation (RPA). Our expression,
derived using the quasiboson approximation, is a straightforward generalization
of the RPA correlation energy. We test the reliability of our expression by
comparing against full diagonalization in 0 h-bar omega shell-model spaces. In
general the RPA values are an improvement over mean-field (Hartree-Fock)
results, but are not always consistent with shell-model results. We also
consider exact symmetries broken in the mean-field state and whether or not
they are restored in RPA.Comment: 7 pages, 3 figure
Transient thermal effects in solid noble gases as materials for the detection of Dark Matter
The transient phenomena produced in solid noble gases by the stopping of the
recoils resulting from the elastic scattering processes of WIMPs from the
galactic halo were modelled, as dependencies of the temperatures of lattice and
electronic subsystems on the distance to the recoil's trajectory, and time from
its passage. The peculiarities of these thermal transients produced in Ar, Kr
and Xe were analysed for different initial temperatures and WIMP energies, and
were correlated with the characteristics of the targets and with the energy
loss of the recoils. The results were compared with the thermal spikes produced
by the same WIMPs in Si and Ge. In the range of the energy of interest, up to
tens of keV for the self-recoil, local phase transitions solid - liquid and
even liquid - gas were found possible, and the threshold parameters were
established.Comment: Minor corrections and updated references; accepted to JCA
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