Ref HAL: hal-00506437_v1
Exporter : BibTex | endNote
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.

Ref HAL: hal-00506428_v1
DOI: 10.1103/PhysRevD.82.024024
WoS: 000280067700005
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28 Citations
Résumé:

We present two results on the recently proposed new spin foam models. First, we show how a (slightly modified) restriction on representations in the Engle-Pereira-Rovelli-Livine model leads to the appearance of the Ashtekar-Barbero connection, thus bringing this model even closer to loop quantum gravity. Second, we however argue that the quantization procedure used to derive the new models is inconsistent since it relies on the symplectic structure of the unconstrained BF theory.

Ref HAL: hal-00468456_v1
Ref Arxiv: 1003.3964
DOI: 10.1007/JHEP06(2010)066
WoS: 000279630800013
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
13 Citations
Résumé:

Recently, an exact description of instanton corrections to the moduli spaces of 4d N=2 supersymmetric gauge theories compactified on a circle and Calabi-Yau compactifications of Type II superstring theories was found. The equations determining the instanton contributions turn out to have the form of Thermodynamic Bethe Ansatz. We explore further this relation and, in particular, we identify the contact potential of quaternionic string moduli space with the free energy of the integrable system and the Kahler potential of the gauge theory moduli space with the Yang-Yang functional. We also show that the corresponding S-matrix satisfies all usual constraints of 2d integrable models, including crossing and bootstrap, and derive the associated Y-system. Surprisingly, in the simplest case the Y-system is described by the MacMahon function relevant for crystal melting and topological strings.

Commentaires: 25 pages, 1 figure

Ref HAL: hal-00442066_v1
Ref Arxiv: 0912.3406
DOI: 10.1063/1.3430574
WoS: 000280854500037
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
14 Citations
Résumé:

Four-dimensional quaternion-Kahler metrics, or equivalently self-dual Einstein spaces M, are known to be encoded locally into one real function h subject to Przanowski's Heavenly equation. We elucidate the relation between this description and the usual twistor description for quaternion-Kahler spaces. In particular, we show that the same space M can be described by infinitely many different solutions h, associated to different complex (local) submanifolds on the twistor space, and therefore to different (local) integrable complex structures on M. We also study quaternion-Kahler deformations of M and, in the special case where M has a Killing vector field, show that the corresponding variations of h are related to eigenmodes of the conformal Laplacian on M. We exemplify our findings on the four-sphere S^4, the hyperbolic plane H^4 and on the "universal hypermultiplet", i.e. the hypermultiplet moduli space in type IIA string compactified on a rigid Calabi-Yau threefold.

Commentaires: 44 pages, 1 figure

Ref HAL: hal-00412948_v1
Exporter : BibTex | endNote
Résumé:

I'll review the recent progress in understanding of non-perturbative effects in Calabi-Yau compactifications of type II string theories. I'll show that combining non-perturbative symmetries and dualities of string theory with a geometric framework based on certain twistor spaces, it is possible to find all D-brane instanton corrections to the hypermultiplet moduli space of compactified string theory. These corrections are encoded in a simple dilogarithm function and have a nice geometric description. Besides, this approach allows also to obtain a non-perturbative generalization of the classical mirror map and has various relations to other aspects of stringy non-perturbative physics.

Ref HAL: hal-00398002_v1
Ref Arxiv: 0906.3743
DOI: 10.1088/1126-6708/2009/09/108
WoS: 000270667600108
Ref. & Cit.: NASA ADS
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23 Citations
Résumé:

Using the twistor approach to hypermultiplet moduli spaces, we derive theworldsheet, D(-1), and D1-instanton contributions to the generalized mirrormap, relating Type IIA and Type IIB string theory compactified on genericmirror Calabi-Yau threefolds. For this purpose, we provide a novel descriptionof the twistor space underlying the Type IIB hypermultiplet moduli space wherethe SL(2,Z)-action is found to be free from quantum corrections. The extent towhich instanton effects may resolve the perturbative singularities of themoduli space metric is discussed.

Ref HAL: hal-00362465_v1
Ref Arxiv: 0902.2761
DOI: 10.1088/1751-8113/42/33/335402
WoS: 000268480000023
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
39 Citations
Résumé:

We present some results on instanton corrections to the hypermultiplet moduli space in Calabi-Yau compactifications of type-II string theories. Previously, using twistor methods, only a class of D-instantons (D2-instantons wrapping A-cycles) was incorporated exactly and the rest was treated only linearly. We go beyond the linear approximation and give a set of holomorphic functions which, through a known procedure, capture the effect of D-instantons at all orders. Moreover, we show that for a sector where all instanton charges have vanishing symplectic invariant scalar product, the hypermultiplet metric can be computed explicitly.

Commentaires: 35 pages, 3 figures, uses JHEP3.cls .