340 research outputs found
An Alternative Topological Field Theory of Generalized Complex Geometry
We propose a new topological field theory on generalized complex geometry in
two dimension using AKSZ formulation. Zucchini's model is model in the case
that the generalized complex structuredepends on only a symplectic structure.
Our new model is model in the case that the generalized complex structure
depends on only a complex structure.Comment: 29 pages, typos and references correcte
Three Dimensional Topological Field Theory induced from Generalized Complex Structure
We construct a three-dimensional topological sigma model which is induced
from a generalized complex structure on a target generalized complex manifold.
This model is constructed from maps from a three-dimensional manifold to an
arbitrary generalized complex manifold . The theory is invariant under the
diffeomorphism on the world volume and the -transformation on the
generalized complex structure. Moreover the model is manifestly invariant under
the mirror symmetry. We derive from this model the Zucchini's two dimensional
topological sigma model with a generalized complex structure as a boundary
action on . As a special case, we obtain three dimensional
realization of a WZ-Poisson manifold.Comment: 18 page
Detecting Precipitation Climate Changes: An Approach Based on a Stochastic Daily Precipitation Model
2002 Mathematics Subject Classification: 62M10.We consider development of daily precipitation models based
on [3] for some sites in Bulgaria. The precipitation process is modelled as
a two-state first-order nonstationary Markov model. Both the probability
of rainfall occurrance and the rainfall intensity are allowed depend on the
intensity on the preceeding day. To investigate the existence of long-term
trend and of changes in the pattern of seasonal variation we use a synthesis
of the methodology presented in [3] and the idea behind the classical running
windows technique for data smoothing. The resulting time series of model
parameters are used to quantify changes in the precipitation process over
the territory of Bulgaria
A heterotic sigma model with novel target geometry
We construct a (1,2) heterotic sigma model whose target space geometry
consists of a transitive Lie algebroid with complex structure on a Kaehler
manifold. We show that, under certain geometrical and topological conditions,
there are two distinguished topological half--twists of the heterotic sigma
model leading to A and B type half--topological models. Each of these models is
characterized by the usual topological BRST operator, stemming from the
heterotic (0,2) supersymmetry, and a second BRST operator anticommuting with
the former, originating from the (1,0) supersymmetry. These BRST operators
combined in a certain way provide each half--topological model with two
inequivalent BRST structures and, correspondingly, two distinct perturbative
chiral algebras and chiral rings. The latter are studied in detail and
characterized geometrically in terms of Lie algebroid cohomology in the
quasiclassical limit.Comment: 83 pages, no figures, 2 references adde
Generalized structures of N=1 vacua
We characterize N=1 vacua of type II theories in terms of generalized complex
structure on the internal manifold M. The structure group of T(M) + T*(M) being
SU(3) x SU(3) implies the existence of two pure spinors Phi_1 and Phi_2. The
conditions for preserving N=1 supersymmetry turn out to be simple
generalizations of equations that have appeared in the context of N=2 and
topological strings. They are (d + H wedge) Phi_1=0 and (d + H wedge) Phi_2 =
F_RR. The equation for the first pure spinor implies that the internal space is
a twisted generalized Calabi-Yau manifold of a hybrid complex-symplectic type,
while the RR-fields serve as an integrability defect for the second.Comment: 21 pages. v2, v3: minor changes and correction
Poisson sigma model on the sphere
We evaluate the path integral of the Poisson sigma model on sphere and study
the correlators of quantum observables. We argue that for the path integral to
be well-defined the corresponding
Poisson structure should be unimodular. The construction of the finite
dimensional BV theory is presented and we argue that it is responsible for the
leading semiclassical contribution. For a (twisted) generalized Kahler manifold
we discuss the gauge fixed action for the Poisson sigma model. Using the
localization we prove that for the holomorphic Poisson structure the
semiclassical result for the correlators is indeed the full quantum result.Comment: 38 page
M-theory on eight-manifolds revisited: N=1 supersymmetry and generalized Spin(7) structures
The requirement of supersymmetry for M-theory backgrounds of the
form of a warped product , where is an eight-manifold
and is three-dimensional Minkowski or AdS space, implies the
existence of a nowhere-vanishing Majorana spinor on . lifts to a
nowhere-vanishing spinor on the auxiliary nine-manifold , where
is a circle of constant radius, implying the reduction of the structure
group of to . In general, however, there is no reduction of the
structure group of itself. This situation can be described in the language
of generalized structures, defined in terms of certain spinors of
. We express the condition for supersymmetry
in terms of differential equations for these spinors. In an equivalent
formulation, working locally in the vicinity of any point in in terms of a
`preferred' structure, we show that the requirement of
supersymmetry amounts to solving for the intrinsic torsion and all irreducible
flux components, except for the one lying in the of , in
terms of the warp factor and a one-form on (not necessarily
nowhere-vanishing) constructed as a bilinear; in addition, is
constrained to satisfy a pair of differential equations. The formalism based on
the group is the most suitable language in which to describe
supersymmetric compactifications on eight-manifolds of structure,
and/or small-flux perturbations around supersymmetric compactifications on
manifolds of holonomy.Comment: 24 pages. V2: introduction slightly extended, typos corrected in the
text, references added. V3: the role of Spin(7) clarified, erroneous
statements thereof corrected. New material on generalized Spin(7) structures
in nine dimensions. To appear in JHE
Induced Polyakov supergravity on Riemann surfaces of higher genus
An effective action is obtained for the , induced supergravity on a
compact super Riemann surface (without boundary) of genus ,
as the general solution of the corresponding superconformal Ward identity. This
is accomplished by defining a new super integration theory on
which includes a new formulation of the super Stokes theorem and residue
calculus in the superfield formalism. Another crucial ingredient is the notion
of polydromic fields. The resulting action is shown to be well-defined and free
of singularities on \sig. As a by-product, we point out a morphism between
the diffeomorphism symmetry and holomorphic properties.Comment: LPTB 93-10, Latex file 20 page
Generalized Kahler Geometry from supersymmetric sigma models
We give a physical derivation of generalized Kahler geometry. Starting from a
supersymmetric nonlinear sigma model, we rederive and explain the results of
Gualtieri regarding the equivalence between generalized Kahler geometry and the
bi-hermitean geometry of Gates-Hull-Rocek.
When cast in the language of supersymmetric sigma models, this relation maps
precisely to that between the Lagrangian and the Hamiltonian formalisms.
We also discuss topological twist in this context.Comment: 18 page
Canonical differential geometry of string backgrounds
String backgrounds and D-branes do not possess the structure of Lorentzian
manifolds, but that of manifolds with area metric. Area metric geometry is a
true generalization of metric geometry, which in particular may accommodate a
B-field. While an area metric does not determine a connection, we identify the
appropriate differential geometric structure which is of relevance for the
minimal surface equation in such a generalized geometry. In particular the
notion of a derivative action of areas on areas emerges naturally. Area metric
geometry provides new tools in differential geometry, which promise to play a
role in the description of gravitational dynamics on D-branes.Comment: 20 pages, no figures, improved journal versio
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