145 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
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
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
The biHermitian topological sigma model
BiHermitian geometry, discovered long ago by Gates, Hull and Roceck, is the
most general sigma model target space geometry allowing for (2,2) world sheet
supersymmetry. By using the twisting procedure proposed by Kapustin and Li, we
work out the type A and B topological sigma models for a general biHermtian
target space, we write down the explicit expression of the sigma model's action
and BRST transformations and present a computation of the topological gauge
fermion and the topological action.Comment: 40 pages, Latex. Analysis of sect. 6 improved; references adde
First-order supersymmetric sigma models and target space geometry
We study the conditions under which N=(1,1) generalized sigma models support
an extension to N=(2,2). The enhanced supersymmetry is related to the target
space complex geometry. Concentrating on a simple situation, related to Poisson
sigma models, we develop a language that may help us analyze more complicated
models in the future. In particular, we uncover a geometrical framework which
contains generalized complex geometry as a special case.Comment: 1+19 pages, JHEP style, published versio
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
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
Topological A-Type Models with Flux
We study deformations of the A-model in the presence of fluxes, by which we
mean rank-three tensors with antisymmetrized upper/lower indices, using the
AKSZ construction. Generically these are topological membrane models, and we
show that the fluxes are related to deformations of the Courant bracket which
generalize the twist by a closed 3-from , in the sense that satisfying the
AKSZ master equation implies the integrability conditions for an almost
generalized complex structure with respect to the deformed Courant bracket. In
addition, the master equation imposes conditions on the fluxes that generalize
. The membrane model can be defined on a large class of - and -structure manifolds, including geometries inspired by
supersymmetric -models with additional supersymmetries due to almost
complex (but not necessarily complex) structures in the target space.
Furthermore, we show that the model can be defined on three particular
half-flat manifolds related to the Iwasawa manifold.
When only -flux is turned on it is possible to obtain a topological string
model, which we do for the case of a Calabi-Yau with a closed 3-form turned on.
The simplest deformation from the A-model is due to the
component of a non-trivial -field. The model is generically no longer
evaluated on holomorphic maps and defines new topological invariants.
Deformations due to -flux can be more radical, completely preventing
auxiliary fields from being integrated out.Comment: 30 pages. v2: Improved Version. References added. v3: Minor changes,
published in JHE
Generalised Geometry for M-Theory
Generalised geometry studies structures on a d-dimensional manifold with a
metric and 2-form gauge field on which there is a natural action of the group
SO(d,d). This is generalised to d-dimensional manifolds with a metric and
3-form gauge field on which there is a natural action of the group .
This provides a framework for the discussion of M-theory solutions with flux. A
different generalisation is to d-dimensional manifolds with a metric, 2-form
gauge field and a set of p-forms for either odd or even on which there is a
natural action of the group . This is useful for type IIA or IIB
string solutions with flux. Further generalisations give extended tangent
bundles and extended spin bundles relevant for non-geometric backgrounds.
Special structures that arise for supersymmetric backgrounds are discussed.Comment: 31 page
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