Ref HAL: hal-00715152_v1
Ref Arxiv: 1207.1109
DOI: 10.1007/JHEP04(2013)002
WoS: 000321208400002
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25 Citations
Résumé:

The D-instanton corrected hypermultiplet moduli space of type II string theory compactified on a Calabi-Yau threefold is known in the type IIA picture to be determined in terms of the generalized Donaldson-Thomas invariants, through a twistorial construction. At the same time, in the mirror type IIB picture, and in the limit where only D3-D1-D(-1)-instanton corrections are retained, it should carry an isometric action of the S-duality group SL(2,Z). We prove that this is the case in the one-instanton approximation, by constructing a holomorphic action of SL(2,Z) on the linearized twistor space. Using the modular invariance of the D4-D2-D0 black hole partition function, we show that the standard Darboux coordinates in twistor space have modular anomalies controlled by period integrals of a Siegel-Narain theta series, which can be canceled by a contact transformation generated by a holomorphic mock theta series.

Commentaires: 42 pages

Ref HAL: hal-00705850_v1
Ref Arxiv: 1206.1341
DOI: 10.1007/JHEP08(2012)112
WoS: 000309883200057
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17 Citations
Résumé:

In type IIB string compactifications on a Calabi-Yau threefold, the hypermultiplet moduli space $M_H$ must carry an isometric action of the modular group SL(2,Z), inherited from the S-duality symmetry of type IIB string theory in ten dimensions. We investigate how this modular symmetry is realized at the level of the twistor space of $M_H$, and construct a general class of SL(2,Z)-invariant quaternion-Kahler metrics with two commuting isometries, parametrized by a suitably covariant family of holomorphic transition functions. This family should include $M_H$ corrected by D3-D1-D(-1)-instantons (with fivebrane corrections ignored) and, after taking a suitable rigid limit, the Coulomb branch of five-dimensional N=2 gauge theories compactified on a torus, including monopole string instantons. These results allow us to considerably simplify the derivation of the mirror map between type IIA and IIB fields in the sector where only D1-D(-1)-instantons are retained.

Commentaires: 29 pages, 1 figure

Ref HAL: hal-00684524_v1
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Résumé:

I'll review a progress in obtaining the complete non-perturbative effective action of type II string theory compactified on a Calabi-Yau manifold. This problem is equivalent to understanding quantum corrections to the metric on the hypermultiplet moduli space. We show how all these corrections, which include D-brane and NS5-brane instantons, are incorporated in the framework of the twistor approach, which provides a powerful mathematical description of hyperkahler and quaternion-Kahler manifolds. I'll also present new insights on S-duality, quantum mirror symmetry, connections to integrable models and topological strings.

Ref HAL: tel-00682454_v1
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Résumé:

Un des aspects fascinants de la théorie des cordes, c'est qu'elle vit dans l'espace-temps de dix dimensions. Mais cela implique que, pour la relier à des observations phénoménologiques, elle devrait ȇtre compactifiées à quatre dimensions. Un cas particulièrement riche, mais toujours faisable correspond à la compactification sur une variété de Calabi-Yau qui donne à basse énergie une théorie effective avec la supersymétrie N=2. L'action de cette théorie est complètement déterminée par la métrique sur son espace des modules qui comporte deux composantes correspondant aux multiplets vectoriels et hypermultiplets. La première est classiquement exacte et bien comprise, alors que la dernière reçoit des corrections quantiques et est connue de porter une géométrie compliquée quaternion-Kählerrienne. Dans cette thèse, nous présentons nos résultats sur la description complète non-perturbative de l'espace des modules des hypermultiplets. Nous montrons comment toutes les corrections quantiques, qui comprennent des contributions perturbatives d'une boucle ainsi que celles non-perturbatives venant des D-branes et NS5-branes, sont incorporées dans le cadre de l'approche twisteurielle. Ce cadre, que nous élaborons ici en détail, fournit une description mathématique puissante des variétés hyperkähleriennes et quaternion-Kähleriennes et il est indispensable pour la formulation de la géométrie non-perturbative de l'espace des modules des hypermultiplets. Nous présentons également de nouveaux résultats sur la dualité-S, symétrie miroir quantique, les connexions à des modèles intégrables et aux cordes topologiques.

Ref HAL: hal-00673769_v1
Ref Arxiv: 1202.5039
DOI: 10.1088/0264-9381/29/14/145018
WoS: 000305810600019
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4 Citations
Résumé:

We show that the degenerate sector of Spin(4) Plebanski formulation of four-dimensional gravity is exactly solvable and describes covariantly embedded SU(2) BF theory. This fact provides its spin foam quantization and allows to test various approaches of imposing the simplicity constraints. Our analysis suggests a unique method of imposing the constraints which leads to a consistent and well defined spin foam model.

Commentaires: 34 pages

Ref HAL: hal-00669542_v1
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Résumé:

We show the existence of a duality between the c-map space describing the universal hypermultiplet at tree level and the matrix model description of two-dimensional string theory compactified at a self-dual radius and perturbed by a sine-Liouville potential. It appears as a particular case of a general relation between the twistor description of four-dimensional quaternionic geometries and the Lax formalism for Toda hierarchy. Furthermore, we give an evidence that the instanton corrections to the c-map metric coming from NS5-branes can be encoded into the Baker-Akhiezer function of the integrable hierarchy.

Ref HAL: hal-00663227_v1
Ref Arxiv: 1201.4392
DOI: 10.1016/j.nuclphysb.2012.05.018
WoS: 000306028700009
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6 Citations
Résumé:

We show the existence of a duality between the c-map space describing the universal hypermultiplet at tree level and the matrix model description of two-dimensional string theory compactified at a self-dual radius and perturbed by a sine-Liouville potential. It appears as a particular case of a general relation between the twistor description of four-dimensional quaternionic geometries and the Lax formalism for Toda hierarchy. Furthermore, we give an evidence that the instanton corrections to the c-map metric coming from NS5-branes can be encoded into the Baker-Akhiezer function of the integrable hierarchy.

Commentaires: 19 pages, 2 figures