798 research outputs found
T-duality and Generalized Kahler Geometry
We use newly discovered N = (2, 2) vector multiplets to clarify T-dualities
for generalized Kahler geometries. Following the usual procedure, we gauge
isometries of nonlinear sigma-models and introduce Lagrange multipliers that
constrain the field-strengths of the gauge fields to vanish. Integrating out
the Lagrange multipliers leads to the original action, whereas integrating out
the vector multiplets gives the dual action. The description is given both in N
= (2, 2) and N = (1, 1) superspace.Comment: 14 pages; published version: some conventions improved, minor
clarification
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
Reduction and construction of Poisson quasi-Nijenhuis manifolds with background
We extend the Falceto-Zambon version of Marsden-Ratiu Poisson reduction to
Poisson quasi-Nijenhuis structures with background on manifolds. We define
gauge transformations of Poisson quasi-Nijenhuis structures with background,
study some of their properties and show that they are compatible with reduction
procedure. We use gauge transformations to construct Poisson quasi-Nijenhuis
structures with background.Comment: to appear in IJGMM
Topological twisted sigma model with H-flux revisited
In this paper we revisit the topological twisted sigma model with H-flux. We
explicitly expand and then twist the worldsheet Lagrangian for bi-Hermitian
geometry. we show that the resulting action consists of a BRST exact term and
pullback terms, which only depend on one of the two generalized complex
structures and the B-field. We then discuss the topological feature of the
model.Comment: 16 pages. Appendix adde
AKSZ construction from reduction data
We discuss a general procedure to encode the reduction of the target space
geometry into AKSZ sigma models. This is done by considering the AKSZ
construction with target the BFV model for constrained graded symplectic
manifolds. We investigate the relation between this sigma model and the one
with the reduced structure. We also discuss several examples in dimension two
and three when the symmetries come from Lie group actions and systematically
recover models already proposed in the literature.Comment: 42 page
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
Deformation Theory of Holomorphic Vector Bundles, Extended Conformal Symmetry and Extensions of 2D Gravity
Developing on the ideas of R. Stora and coworkers, a formulation of two
dimensional field theory endowed with extended conformal symmetry is given,
which is based on deformation theory of holomorphic and Hermitian spaces. The
geometric background consists of a vector bundle over a closed surface
endowed with a holomorphic structure and a Hermitian structure
subordinated to it. The symmetry group is the semidirect product of the
automorphism group of and the extended Weyl group of and acts on the holomorphic and Hermitian structures. The
extended Weyl anomaly can be shifted into an automorphism chirally split
anomaly by adding to the action a local counterterm, as in ordinary conformal
field theory. The dependence on the scale of the metric on the fiber of is
encoded in the Donaldson action, a vector bundle generalization of the
Liouville action. The Weyl and automorphism anomaly split into two
contributions corresponding respectively to the determinant and
projectivization of . The determinant part induces an effective ordinary
Weyl or diffeomorphism anomaly and the induced central charge can be computed.Comment: 49 pages, plain TeX. A number of misprints have been correcte
The Lie algebroid Poisson sigma model
The Poisson--Weil sigma model, worked out by us recently, stems from gauging
a Hamiltonian Lie group symmetry of the target space of the Poisson sigma
model. Upon gauge fixing of the BV master action, it yields interesting
topological field theories such as the 2--dimensional Donaldson-Witten
topological gauge theory and the gauged A topological sigma model. In this
paper, generalizing the above construction, we construct the Lie algebroid
Poisson sigma model. This is yielded by gauging a Hamiltonian Lie groupoid
symmetry of the Poisson sigma model target space. We use the BV quantization
approach in the AKSZ geometrical version to ensure consistent quantization and
target space covariance. The model has an extremely rich geometry and an
intricate BV cohomology, which are studied in detail.Comment: 52 pages, Late
Gauging the Poisson sigma model
We show how to carry out the gauging of the Poisson sigma model in an AKSZ
inspired formulation by coupling it to the a generalization of the Weil model
worked out in ref. arXiv:0706.1289 [hep-th]. We call the resulting gauged field
theory, Poisson--Weil sigma model. We study the BV cohomology of the model and
show its relation to Hamiltonian basic and equivariant Poisson cohomology. As
an application, we carry out the gauge fixing of the pure Weil model and of the
Poisson--Weil model. In the first case, we obtain the 2--dimensional version of
Donaldson--Witten topological gauge theory, describing the moduli space of flat
connections on a closed surface. In the second case, we recover the gauged A
topological sigma model worked out by Baptista describing the moduli space of
solutions of the so--called vortex equations.Comment: 49 pages, no figures. Typos corrected. Presentation improve
Supersymmetric Oscillator: Novel Symmetries
We discuss various continuous and discrete symmetries of the supersymmetric
simple harmonic oscillator (SHO) in one (0 + 1)-dimension of spacetime and show
their relevance in the context of mathematics of differential geometry. We show
the existence of a novel set of discrete symmetries in the theory which has,
hitherto, not been discussed in the literature on theoretical aspects of SHO.
We also point out the physical relevance of our present investigation.Comment: REVTeX file, 5 pages, minor changes in title, text and abstract,
references expanded, version to appear in EP
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