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
Exporter : BibTex | endNote
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 .

Ref HAL: hal-00349154_v1
Ref Arxiv: 0812.4219
DOI: 10.1088/1126-6708/2009/03/044
WoS: 000265600800044
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
55 Citations
Résumé:

Finding the exact, quantum corrected metric on the hypermultiplet moduli space in Type II string compactifications on Calabi-Yau threefolds still poses an outstanding open problem. We address this issue by relating the quaternionic-Kahler metric on the hypermultiplet moduli space to the complex contact geometry on its twistor space. In this framework, Euclidean D-brane instanton contributions are captured by contact transformations between different locally flat patches. We derive those by recasting the previously known A-type D2-instanton corrections in the language of contact geometry, covariantizing the result under electro-magnetic duality, and using mirror symmetry. As a result, we are able to express the effects of all D-instantons in Type II compactifications concisely as a sum of dilogarithm functions. We conclude with some comments on the relation to microscopic degeneracies of four-dimensional BPS black holes and to the wall-crossing formula of Kontsevich and Soibelman, and on the form of the yet unknown NS5-brane instanton contributions.

Ref HAL: hal-00328291_v1
Ref Arxiv: 0810.1675
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
Résumé:

We extend the twistor methods developed in our earlier work on linear deformations of hyperkahler manifolds [arXiv:0806.4620] to the case of quaternionic-Kahler manifolds. Via Swann's construction, deformations of a 4d-dimensional quaternionic-Kahler manifold $M$ are in one-to-one correspondence with deformations of its $4d+4$-dimensional hyperkahler cone $S$. The latter can be encoded in variations of the complex symplectomorphisms which relate different locally flat patches of the twistor space $Z_S$, with a suitable homogeneity condition that ensures that the hyperkahler cone property is preserved. Equivalently, we show that the deformations of $M$ can be encoded in variations of the complex contact transformations which relate different locally flat patches of the twistor space $Z_M$ of $M$, by-passing the Swann bundle and its twistor space. We specialize these general results to the case of quaternionic-Kahler metrics with $d+1$ commuting isometries, obtainable by the Legendre transform method, and linear deformations thereof. We illustrate our methods for the hypermultiplet moduli space in string theory compactifications at tree- and one-loop level.

Commentaires: 55 pages, 1 figure, uses JHEP3.cls