Résumé:

I'll review the progress achieved in constructing the non-perturbative hypermultiplet moduli space using twistorial methods. The metric on this space determines the low-energy effective action of Type II string theory compactified on a Calabi-Yau threefold. It receives instanton corrections due to D-branes and NS5-branes and I'll show how all of them can be nicely incorporated at the level of the twistor space. However, so far this construction has provided NS5-instantons only in the one-instanton approximation, so that they represent the last missing piece of the full non-perturbative picture. I'll argue that the inclusion of these corrections may be closely related to quantization of a certain integrable structure.

Ref HAL: hal-00808906_v1
Ref Arxiv: 1304.0766
DOI: 10.1090/pspum/090/01523
WoS: WOS:000376419100009
Ref. & Cit.: NASA ADS
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15 Citations
Résumé:

The hypermultiplet moduli space M_H in type II string theories compactified on a Calabi-Yau threefold X is largely constrained by supersymmetry (which demands quaternion-Kählerity), S-duality (which requires an isometric action of SL(2, Z)) and regularity. Mathematically, M_H ought to encode all generalized Donaldson-Thomas invariants on X consistently with wall-crossing, modularity and homological mirror symmetry. We review recent progress towards computing the exact metric on M_H, or rather the exact complex contact structure on its twistor space.

Commentaires: 31 pages; Contribution to the Proceedings of String Math 2012

Ref HAL: hal-00862720_v1
Ref Arxiv: 1308.6586
DOI: 10.1007/s10714-013-1639-1
WoS: 000333634900026
Ref. & Cit.: NASA ADS
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23 Citations
Résumé:

We perform the complete canonical analysis of the tetrad formulation of bimetric gravity and confirm that it is ghost-free describing the seven degrees of freedom of a massless and a massive gravitons. In particular, we find explicit expressions for secondary constraints, one of which is responsible for removing the ghost, whereas the other ensures the equivalence with the metric formulation. Both of them have a remarkably simple form and, being combined with conditions on Lagrange multipliers, can be written in a covariant way.

Ref HAL: hal-00834815_v1
Ref Arxiv: 1306.1837
DOI: 10.1063/1.4826603
WoS: 000326638100015
Ref. & Cit.: NASA ADS
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7 Citations
Résumé:

We provide an explicit twistorial construction of quaternion-Kahler manifolds obtained by deformation of c-map spaces and carrying an isometric action of the modular group SL(2,Z). The deformation is not assumed to preserve any continuous isometry and therefore this construction presents a general framework for describing NS5-brane instanton effects in string compactifications with N=2 supersymmetry. In this context the modular invariant parametrization of twistor lines found in this work yields the complete non-perturbative mirror map between type IIA and type IIB physical fields.

Commentaires: 28 pages. We are grateful to Carlos Contou-Carrere, Daniel Persson, and Boris Pioline for useful discussions.

Ref HAL: hal-00766632_v1
Ref Arxiv: 1212.3614
DOI: 10.1007/JHEP06(2013)068
WoS: WOS:000321381800014
Ref. & Cit.: NASA ADS
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22 Citations
Résumé:

We propose and study a new first order version of the ghost-free massive gravity. Instead of metrics or tetrads, it uses a connection together with Plebanski's chiral 2-forms as fundamental variables, rendering the phase space structure similar to that of SU(2) gauge theories. The chiral description simplifies computations of the constraint algebra, and allows us to perform the complete canonical analysis of the system. In particular, we explicitly compute the secondary constraint and carry out the stabilization procedure, thus proving that in general the theory propagates 7 degrees of freedom, consistently with previous claims. Finally, we point out that the description in terms of 2-forms opens the door to an infinite class of ghost-free massive bi-gravity actions.

Commentaires: 25 pages

Ref HAL: hal-00742034_v1
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Résumé:

The hypermultiplet moduli space of type IIB string theory compactified on a Calabi-Yau threefold is known to receive various instanton corrections and to carry an isometric action of SL(2,Z) duality group. The instanton corrections are most easily incorporated in the mirror type IIA formulation using the twistor space construction of quaternion-Kahler manifolds. In this talk I'll show how this construction can be turned into an explicitly S-duality invariant form thereby recovering the instanton corrections in type IIB and the quantum corrected mirror map between the physical fields of the two formulations. In particular, the case of D3-instantons reveals the importance of Mock theta series and period integrals which provide a holomorphic realization of S-duality in the twistor space.

Ref HAL: hal-00741850_v1
Ref Arxiv: 1210.3037
DOI: 10.1007/JHEP03(2013)085
WoS: 000317521200085
Ref. & Cit.: NASA ADS
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3 Citations
Résumé:

Heterotic string theory compactified on a K3 surface times T^2 is believed to be equivalent to type II string theory on a suitable Calabi-Yau threefold. In particular, it must share the same hypermultiplet moduli space. Building on the known twistorial description on the type II side, and on recent progress on the map between type II and heterotic moduli in the 'double scaling' limit (where both the type II and heterotic strings become classical), we provide a new twistorial construction of the hypermultiplet moduli space in this limit which is adapted to the symmetries of the heterotic string. We also take steps towards understanding the twistorial description for heterotic worldsheet instanton corrections away from the double scaling limit. As a spin-off, we obtain a twistorial description of a class of automorphic forms of SO(4,n,Z) obtained by Borcherds' lift.

Commentaires: 30 pages