Ref HAL: hal-00609343_v1
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We present a review of our work on instanton corrections to the hypermultiplet moduli space of Calabi-Yau compactifications of type II string theories with particular emphasis on the realization of S-duality and mirror symmetry at the non-perturbative level.

Ref HAL: hal-00543669_v1
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The low-energy effective action of compactified Type II string theory is determined by the geometry of its moduli space which receives instanton corrections. I'll present a non-perturbative description of this moduli space, which crucially relies on the twistor approach to quaternionic geometries. Using this approach, I'll show how one can incorporate contributions from all D-brane instantons and give some partial results on instanton effects generated by NS5-brane. I'll argue that, ignoring the latter contributions, the moduli space corresponds to an integrable system.

Ref HAL: hal-00531360_v1
Ref Arxiv: 1010.5792
DOI: 10.1007/JHEP03(2011)111
WoS: 000289295300039
Ref. & Cit.: NASA ADS
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35 Citations
Résumé:

We investigate quantum corrections to the hypermultiplet moduli space M in Calabi-Yau compactifications of type II string theories, with particular emphasis on instanton effects from Euclidean NS5-branes. Based on the consistency of D- and NS5-instanton corrections, we determine the topology of the hypermultiplet moduli space at fixed string coupling and Calabi-Yau metric, as previewed in arXiv:1009.3026. On the type IIB side, we compute corrections from (p,k)-fivebrane instantons to the metric on M (specifically, the correction to the complex contact structure on its twistor space Z) by applying S-duality to the D-instanton sum. For fixed fivebrane charge k, the corrections can be written as a non-Gaussian theta series, whose summand for k=1 reduces to the topological A-model amplitude. By mirror symmetry, instanton corrections induced from the chiral type IIA NS5-brane are similarly governed by the wave function of the topological B-model. In the course of this investigation we clarify charge quantization for coherent sheaves and find hitherto unnoticed corrections to the Heisenberg, monodromy and S-duality actions on M, as well as to the mirror map for Ramond-Ramond fields and D-brane charges.

Commentaires: 73 pages

Ref HAL: hal-00526407_v1
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I'll review the twistor approach to the description of hyperkahler and quaternion-Kahler geometries allowing their efficient parametrization in terms of a set of holomorphic potentials. These geometries appear as moduli spaces in N=2 supersymmetric gauge theories and in compactifications of Type II superstring theories on Calabi-Yau threefolds. In particular, using the twistor approach, I'll present a non-perturbative description of the hypermultiplet moduli space, which determines the low energy effective action of compactified string theory. The geometry of this moduli space gets instanton corrections due to various branes wrapping non-trivial cycles of the Calabi-Yau. I'll show how one can describe all instantons coming from D-branes and tentative results on instanton contributions from NS5-branes. These results are used to get a quantum completion of the classical mirror map and to show a deep relation of the twistor description of D-instantons to integrable models. In particular, I'll show that the D-instanton corrections are described by Thermodynamic Bethe Ansatz and the corresponding S-matrix satisfies all axioms of integrability.

Ref HAL: hal-00520869_v1
Ref Arxiv: 1009.4475
DOI: 10.1016/j.physrep.2011.05.002
WoS: 000295430400001
Ref. & Cit.: NASA ADS
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28 Citations
Résumé:

This is a review of the present status of loop and spin foam approaches to quantization of four-dimensional general relativity. It aims at raising various issues which seem to challenge some of the methods and the results often taken as granted in these domains. A particular emphasis is given to the issue of diffeomorphism and local Lorentz symmetries at the quantum level and to the discussion of new spin foam models. We also describe modifications of these two approaches which may overcome their problems and speculate on other promising research directions.

Commentaires: 75 pages

Ref HAL: hal-00518356_v1
Ref Arxiv: 1009.3026
DOI: 10.1103/PhysRevD.83.026001
WoS: 000286770900003
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
16 Citations
Résumé:

By analyzing qualitative aspects of NS5-brane instanton corrections, we determine the topology of the hypermultiplet moduli space M_H in Calabi-Yau compactifications of type II string theories at fixed value of the dilaton and of the Calabi-Yau metric. Specifically, we show that for fivebrane instanton couplings to be well-defined, translations along the intermediate Jacobian must induce non-trivial shifts of the Neveu-Schwarz axion which had thus far been overlooked. As a result, the Neveu-Schwarz axion parametrizes the fiber of a circle bundle, isomorphic to the one in which the fivebrane partition function is valued. In a companion paper [1], we go beyond the present analysis and take steps towards a quantitative description of fivebrane instanton corrections, using a combination of mirror symmetry, S-duality, topological string theory and twistor techniques.

Commentaires: 5 pages

Ref HAL: hal-00515368_v1
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Résumé:

I'll present recent results on the non-perturbative description of the hypermultiplet moduli space of compactified Type II string theory. The geometry of the moduli space gets instanton corrections due to D-branes and I'll show how one can describe all these D-instantons using the twistor approach to quaternionic geometries. These results are used to get a quantum completion of the classical mirror map and to show a deep relation of the twistor description of D-instantons to integrability.