3,648 research outputs found
On Semi-Periods
The periods of the three-form on a Calabi-Yau manifold are found as solutions
of the Picard-Fuchs equations; however, the toric varietal method leads to a
generalized hypergeometric system of equations which has more solutions than
just the periods. This same extended set of equations can be derived from
symmetry considerations. Semi-periods are solutions of this extended system.
They are obtained by integration of the three-form over chains; these chains
can be used to construct cycles which, when integrated over, give periods. In
simple examples we are able to obtain the complete set of solutions for the
extended system. We also conjecture that a certain modification of the method
will generate the full space of solutions in general.Comment: 18 pages, plain TeX. Revised derivation of system of
equations; version to appear in Nuclear Physics
On Periods for String Compactifications
Motivated by recent developments in the computation of periods for string
compactifications with , we develop a complementary method which also
produces a convenient basis for related calculations. The models are realized
as Calabi--Yau hypersurfaces in weighted projective spaces of dimension four or
as Landau-Ginzburg vacua. The calculation reproduces known results and also
allows a treatment of Landau--Ginzburg orbifolds with more than five fields.Comment: HUPAPP-93/6, IASSNS-HEP-93/80, UTTG-27-93. 21 pages,harvma
Relating the Cosmological Constant and Supersymmetry Breaking in Warped Compactifications of IIB String Theory
It has been suggested that the observed value of the cosmological constant is
related to the supersymmetry breaking scale M_{susy} through the formula Lambda
\sim M_p^4 (M_{susy}/M_p)^8. We point out that a similar relation naturally
arises in the codimension two solutions of warped space-time varying
compactifications of string theory in which non-isotropic stringy moduli induce
a small but positive cosmological constant.Comment: 7 pages, LaTeX, references added and minor changes made, (v3) map
between deSitter and global cosmic brane solutions clarified, supersymmetry
breaking discussion improved and references adde
Mechanics of universal horizons
Modified gravity models such as Ho\v{r}ava-Lifshitz gravity or
Einstein-{\ae}ther theory violate local Lorentz invariance and therefore
destroy the notion of a universal light cone. Despite this, in the infrared
limit both models above possess static, spherically symmetric solutions with
"universal horizons" - hypersurfaces that are causal boundaries between an
interior region and asymptotic spatial infinity. In other words, there still
exist black hole solutions. We construct a Smarr formula (the relationship
between the total energy of the spacetime and the area of the horizon) for such
a horizon in Einstein-{\ae}ther theory. We further show that a slightly
modified first law of black hole mechanics still holds with the relevant area
now a cross-section of the universal horizon. We construct new analytic
solutions for certain Einstein-{\ae}ther Lagrangians and illustrate how our
results work in these exact cases. Our results suggest that holography may be
extended to these theories despite the very different causal structure as long
as the universal horizon remains the unique causal boundary when matter fields
are added.Comment: Minor clarifications. References update
AdS2xS2 as an exact heterotic string background
An exact heterotic string theory on an AdS2xS2 background supported by an
electromagnetic flux is found as a marginal deformation of an SL(2,R)xSU(2) WZW
model. Based on a talk given at NATO Advanced Study Institute and EC Summer
School on String Theory: from Gauge Interactions to Cosmology, Cargese,
Corsica, France, 7 Jun - 19 Jun 2004.Comment: 5 page
On supersymmetric Minkowski vacua in IIB orientifolds
Supersymmetric Minkowski vacua in IIB orientifold compactifications based on
orbifolds with background fluxes and non-perturbative superpotentials are
investigated. Especially, microscopic requirements and difficulties to obtain
such vacua are discussed. We show that orbifold models with one and two complex
structure moduli and supersymmetric 2-form flux can be successfully stabilized
to such vacua. By taking additional gaugino condensation on fixed space-time
filling D3-branes into account also models without complex structure can be
consistently stabilized to Minkowski vacua.Comment: 17 pages, 2 figures; More detailed proof for absence of complex flat
directions in susy AdS vacua given; Footnotes and reference adde
Deformed Quantum Cohomology and (0,2) Mirror Symmetry
We compute instanton corrections to correlators in the genus-zero topological
subsector of a (0,2) supersymmetric gauged linear sigma model with target space
P1xP1, whose left-moving fermions couple to a deformation of the tangent
bundle. We then deduce the theory's chiral ring from these correlators, which
reduces in the limit of zero deformation to the (2,2) ring. Finally, we compare
our results with the computations carried out by Adams et al.[ABS04] and Katz
and Sharpe[KS06]. We find immediate agreement with the latter and an
interesting puzzle in completely matching the chiral ring of the former.Comment: AMSLatex, 30 pages, one eps figure. V4: typos corrected, final
version appearing in JHE
A mathematical framework for critical transitions: normal forms, variance and applications
Critical transitions occur in a wide variety of applications including
mathematical biology, climate change, human physiology and economics. Therefore
it is highly desirable to find early-warning signs. We show that it is possible
to classify critical transitions by using bifurcation theory and normal forms
in the singular limit. Based on this elementary classification, we analyze
stochastic fluctuations and calculate scaling laws of the variance of
stochastic sample paths near critical transitions for fast subsystem
bifurcations up to codimension two. The theory is applied to several models:
the Stommel-Cessi box model for the thermohaline circulation from geoscience,
an epidemic-spreading model on an adaptive network, an activator-inhibitor
switch from systems biology, a predator-prey system from ecology and to the
Euler buckling problem from classical mechanics. For the Stommel-Cessi model we
compare different detrending techniques to calculate early-warning signs. In
the epidemics model we show that link densities could be better variables for
prediction than population densities. The activator-inhibitor switch
demonstrates effects in three time-scale systems and points out that excitable
cells and molecular units have information for subthreshold prediction. In the
predator-prey model explosive population growth near a codimension two
bifurcation is investigated and we show that early-warnings from normal forms
can be misleading in this context. In the biomechanical model we demonstrate
that early-warning signs for buckling depend crucially on the control strategy
near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio
Elevating the Free-Fermion Orbifold Model to a Compactification of F-Theory
We study the elliptic fibrations of some Calabi-Yau three-folds, including
the orbifold with , which is
equivalent to the common framework of realistic free-fermion models, as well as
related orbifold models with and (31,7). However,
two related puzzles arise when one considers the
model as an F-theory compactification to six dimensions. The condition for the
vanishing of the gravitational anomaly is not satisfied, suggesting that the
F-theory compactification does not make sense, and the elliptic fibration is
well defined everywhere except at four singular points in the base. We
speculate on the possible existence of N=1 tensor and hypermultiplets at these
points which would cancel the gravitational anomaly in this case.Comment: 19 pages. Standard Latex. The lack of global section for the (27,3)
model is emphasized, as well as a possible relation with the gravitational
anomal
Fermion Zero Modes in the Presence of Fluxes and a Non-perturbative Superpotential
We study the effect of background fluxes of general Hodge type on the
supersymmetry conditions and on the fermionic zero modes on the world-volume of
a Euclidean M5/D3-brane in M-theory/type IIB string theory.
Using the naive susy variation of the modulino fields to determine the number
of zero modes in the presence of a flux of general Hodge type, an inconsistency
appears. This inconsistency is resolved by a modification of the supersymmetry
variation of the modulinos, which captures the back-reaction of the
non-perturbative effects on the background flux and the geometry.Comment: 21 pages, revised version contains a new appendix on dimensional
reduction of spinors and some changes in the spinor equation
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