Isotropic A-branes and the stability condition

Chiantese, Stefano

doi:10.1088/1126-6708/2005/02/003

Cited by 7 publications

(7 citation statements)

References 18 publications

(41 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the other extreme case of J = J ω , it yields all possible types of A-branes, including the non-Lagrangian ones [37,38]. These are two tests of the idea that D-branes in generalized geometries are generalized submanifolds.…”

Section: D-branes As Generalized Complex Submanifoldsmentioning

confidence: 99%

T-duality with H-flux: Non-commutativity, T-folds and structure

Grange

Schäfer‐Nameki

2007

Nuclear Physics B

View full text Add to dashboard Cite

Various approaches to T-duality with NSNS three-form flux are reconciled. Non-commutative torus fibrations are shown to be the open-string version of T-folds. The non-geometric T-dual of a three-torus with uniform flux is embedded into a generalized complex six-torus, and the non-geometry is probed by D0-branes regarded as generalized complex submanifolds. The noncommutativity scale, which is present in these compactifications, is given by a holomorphic Poisson bivector that also encodes the variation of the dimension of the world-volume of D-branes under monodromy. This bivector is shown to exist in SU(3) × SU(3) structure compactifications, which have been proposed as mirrors to NSNS-flux backgrounds. The two SU(3)-invariant spinors are generically not parallel, thereby giving rise to a non-trivial Poisson bivector. Furthermore we show that for non-geometric T-duals, the Poisson bivector may not be decomposable into the tensor product of vectors. IntroductionCompactifications with H-flux are known to give rise to topology changes and even to nongeometric situations when T-duality is performed along directions which have non-trivial support of the NSNS H-flux [1,2,3,4,5,6,7,8]. Non-geometry occurs for example in the very simple situation of a three-torus endowed with an H-flux proportional to its volume form. Consider namely the three-torus as a trivial T 2 -fibration over a circle. Upon T-duality along the fibre, the metric picks up a factor that makes it shrink under monodromy around the base circle. The monodromy around the base is a non-trivial element of the O(2, 2; Z) group acting on the two-torus. This prevents a three-dimensional global Riemannian description from existing. Further T-dualizing along the base leads to more pathological situations, where points do not exist even in a local coordinate patch, and the fibres are conjectured to become non-associative [9,10]. We will restrict ourselves to the case of two T-dualities, and assume that local coordinate patches do exist. Progress in the description of non-associative T-duals was achieved in the recent paper [11], which also contains observations on the open-string metric and non-commutativity for two T-dualities that have some overlap with ours.Essentially three conjectures have been put forward for the description of the T-dual of a torus with H-flux: 1 (I) Field of non-commutative tori: Mathai and Rosenberg proposed that T-dualizing along a two-torus with non-zero H-flux yields a fibration by (or more precisely: field of) noncommutative tori. In particular, this fibration is encoded in a closed one-form, which is obtained by integrating the NSNS flux along the fibre directions [7,12,13].(II) T-folds: these are spaces where T-dualities can act as transition functions between local patches [8]. The T-dualized directions are doubled, and T-duality transformations may patch the doubled fibres together. A sigma model with a T-fold as its target space was proposed, and its boundary conditions were studied in [14,15,16,17,18].(III) G × G struc...

show abstract

Section: D-branes As Generalized Complex Submanifoldsmentioning

confidence: 99%

T-duality with H-flux: Non-commutativity, T-folds and structure

Grange

Schäfer‐Nameki

2007

Nuclear Physics B

View full text Add to dashboard Cite

show abstract

“…A study of the extended Hitchin functional for generalized complex structures, as opposed to ordinary ones, is also natural because the total moduli space of topological B-strings includes the space of complex structures, but has other directions as well, corresponding to the sheaf cohomology groups H q ∂ ( p (T X 1,0 )), where the case of p = q = 1 yields the Beltrami differentials -deformations of the complex structure. See also [16,[18][19][20][21][22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

The Hitchin Functionals and the Topological B-Model at One Loop

2005

View full text Add to dashboard Cite

The quantization in quadratic order of the Hitchin functional, which defines by critical points a Calabi-Yau structure on a six-dimensional manifold, is performed. The conjectured relation between the topological B-model and the Hitchin functional is studied at one loop. It is found that the genus one free energy of the topological B-model disagrees with the one-loop free energy of the minimal Hitchin functional. However, the topological B-model does agree at one-loop order with the extended Hitchin functional, which also defines by critical points a generalized Calabi-Yau structure. The dependence of the one-loop result on a background metric is studied, and a gravitational anomaly is found for both the B-model and the extended Hitchin model. The anomaly reduces to a volume-dependent factor if one computes for only Ricci-flat Kahler metrics. * On leave of absense from ITEP, 117259, Moscow, Russia 7 When the cohomology groups are nonzero, they contribute to Z HE an additional factor

show abstract

“…In fact, it includes as particular cases all known examples of topological branes, including the coisotropic ones. However, to the best of our knowledge, not much has been attempted in this direction so far [10,15,23].…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, generalized complex geometry, which unifies these two types of geometry, may provide a natural mathematical framework for a unified understanding of them. It is also conceivable that topological sigma models with generalized Kaehler targets may exhibit the form of generalized mirror symmetry encountered in flux compactifications of superstring theory [10][11][12][13][14][15]. D-branes are extended solitonic objects of the superstring spectrum, which are expected to play an important role in the ultimate non perturbative understanding of superstring physics.…”

Section: Introductionmentioning

confidence: 99%

Generalized complex geometry, generalized branes and the Hitchin sigma model

Zucchini

2005

J. High Energy Phys.

View full text Add to dashboard Cite

Hitchin's generalized complex geometry has been shown to be relevant in compactifications of superstring theory with fluxes and is expected to lead to a deeper understanding of mirror symmetry. Gualtieri's notion of generalized complex submanifold seems to be a natural candidate for the description of branes in this context. Recently, we introduced a field theoretic realization of generalized complex geometry, the Hitchin sigma model, extending the well known Poisson sigma model. In this paper, exploiting Gualtieri's formalism, we incorporate branes into the model. A detailed study of the boundary conditions obeyed by the world sheet fields is provided. Finally, it is found that, when branes are present, the classical Batalin-Vilkovisky cohomology contains an extra sector that is related non trivially to a novel cohomology associated with the branes as generalized complex submanifolds.

show abstract

Isotropic A-branes and the stability condition

Cited by 7 publications

References 18 publications

T-duality with H-flux: Non-commutativity, T-folds and structure

T-duality with H-flux: Non-commutativity, T-folds and structure

The Hitchin Functionals and the Topological B-Model at One Loop

Generalized complex geometry, generalized branes and the Hitchin sigma model

Contact Info

Product

Resources

About