289 research outputs found
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
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
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
A sigma model field theoretic realization of Hitchin's generalized complex geometry
We present a sigma model field theoretic realization of Hitchin's generalized
complex geometry, which recently has been shown to be relevant in
compactifications of superstring theory with fluxes. Hitchin sigma model is
closely related to the well known Poisson sigma model, of which it has the same
field content. The construction shows a remarkable correspondence between the
(twisted) integrability conditions of generalized almost complex structures and
the restrictions on target space geometry implied by the Batalin--Vilkovisky
classical master equation. Further, the (twisted) classical Batalin--Vilkovisky
cohomology is related non trivially to a generalized Dolbeault cohomology.Comment: 28 pages, Plain TeX, no figures, requires AMS font files AMSSYM.DEF
and amssym.tex. Typos in eq. 6.19 and some spelling correcte
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