Ref HAL: hal-00653555_v1
Ref Arxiv: 1112.1961
DOI: 10.3842/SIGMA.2012.055
WoS: 000307829600001
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
48 Citations
Résumé:

This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the three-dimensional context, where the two approaches are in good agreement, we show how the canonical quantization à la Witten of Riemannian gravity with a positive cosmological constant is related to the Turaev-Viro spin foam model, and how the Ponzano-Regge amplitudes are related to the physical scalar product of Riemannian loop quantum gravity without cosmological constant. In the four-dimensional case, we recall a Lorentz-covariant formulation of loop quantum gravity using projected spin networks, compare it with the new spin foam models, and identify interesting relations and their pitfalls. Finally, we discuss the properties which a spin foam model is expected to possess in order to be consistent with the canonical quantization, and suggest a new model illustrating these results.

Commentaires: 88 pages. Invited review for SIGMA Special Issue "Loop Quantum Gravity and Cosmology"

Ref HAL: hal-00642280_v1
Ref Arxiv: 1111.2892
DOI: 10.1016/j.physrep.2012.09.005
WoS: 000314087300001
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
38 Citations
Résumé:

We 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. We also present new insights on S-duality, quantum mirror symmetry, connections to integrable models and topological strings.

Commentaires: 98 pages

Ref HAL: hal-00630135_v1
Ref Arxiv: 1110.0466
DOI: 10.1007/JHEP12(2011)027
WoS: 000298847200027
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
26 Citations
Résumé:

When formulated in twistor space, the D-instanton corrected hypermultiplet moduli space in N=2 string vacua and the Coulomb branch of rigid N=2 gauge theories on R^3 x S^1 are strikingly similar and, to a large extent, dictated by consistency with wall-crossing. We elucidate this similarity by showing that these two spaces are related under a general duality between, on one hand, quaternion-Kähler manifolds with a quaternionic isometry and, on the other hand, hyperkähler manifolds with a rotational isometry, further equipped with a hyperholomorphic circle bundle with a connection. We show that the transition functions of the hyperholomorphic circle bundle relevant for the hypermultiplet moduli space are given by the Rogers dilogarithm function, and that consistency across walls of marginal stability is ensured by the motivic wall-crossing formula of Kontsevich and Soibelman. We illustrate the construction on some simple examples of wall-crossing related to cluster algebras for rank 2 Dynkin quivers. In an appendix we also provide a detailed discussion on the general relation between wall-crossing and the theory of cluster algebras.

Commentaires: 67 pages, 1 figure

Ref HAL: hal-00626953_v1
Exporter : BibTex | endNote
Résumé:

I'll give a critical review of the present status and recent progress of loop and spin foam approaches to quantization of four-dimensional general relativity, and raise various issues which challenge some of the methods and the results in these domains. In particular, I'll argue that there are indications that the present realization of the loop quantization provided by LQG might be anomalous, whereas the quantization strategy employed in the most of spin foam models is inconsistent with the rules of canonical quantization. On the other hand, I'll suggest modifications of these two approaches which may overcome their problems.

Ref HAL: hal-00626950_v1
Exporter : BibTex | endNote
Résumé:

I'll present an introduction to the spin foam approach to quantum gravity, describe the new spin foam models, their achievements as well as their drawbacks from the point of view of canonical quantization.

Ref HAL: hal-00609343_v1
Exporter : BibTex | endNote
Résumé:

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
Exporter : BibTex | endNote
Résumé:

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.