Résumé:

I'll review the current understanding of the low energy effective theory resulting from compactifications of Type II superstrings on Calabi-Yau manifolds. The effective action can be encoded into the metric on a moduli space which is known to receive quantum stringy corrections, both perturbative and non-perturbative. I'll show how the non-perturbative geometry of this moduli space can be described using twistorial techniques. In the end, I'll argue that the instanton effects coming from NS5-branes, whose understanding is still very incomplete, might be related to a quantization of a certain integrable structure.

Résumé:

I'll review the current understanding of the low energy effective theory resulting from compactifications of Type II superstrings on Calabi-Yau manifolds. The effective action can be encoded into the metric on a moduli space which is known to receive quantum stringy corrections, both perturbative and non-perturbative. I'll show how the non-perturbative geometry of this moduli space can be described using twistorial techniques. In the end, I'll argue that the instanton effects coming from NS5-branes, whose understanding is still very incomplete, might be related to a quantization of a certain integrable structure.

Ref HAL: hal-01229341_v1
Ref Arxiv: 1511.02892
DOI: 10.1007/s11005-016-0857-3
WoS: 000379609000002
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
2 Citations
Résumé:

Motivated by mathematical structures which arise in string vacua and gauge theories with N=2 supersymmetry, we study the properties of certain generalized theta series which appear as Fourier coefficients of functions on a twisted torus. In Calabi-Yau string vacua, such theta series encode instanton corrections from $k$ Neveu-Schwarz five-branes. The theta series are determined by vector-valued wave-functions, and in this work we obtain the transformation of these wave-functions induced by Kontsevich-Soibelman symplectomorphisms. This effectively provides a quantum version of these transformations, where the quantization parameter is inversely proportional to the five-brane charge $k$. Consistency with wall-crossing implies a new five-term relation for Faddeev's quantum dilogarithm $\Phi_b$ at $b=1$, which we prove. By allowing the torus to be non-commutative, we obtain a more general five-term relation valid for arbitrary $b$ and $k$, which may be relevant for the physics of five-branes at finite chemical potential for angular momentum.

Commentaires: 26 pages

Ref HAL: hal-01163853_v1
Exporter : BibTex | endNote
Résumé:

I consider the problem of consistent implementation of symmetries at the non-perturbative level in type II string theory compactifed on a Calabi-Yau threefold. After inclusion of all quantum corrections, all continuous isometries of the classical moduli space are broken to discrete subgroups. I show that the naive choice of these subgroups does not generate a consistent group action, which however can be achieved by taking into account various subtle contributions determined by topological data on the Calabi-Yau. In particular, the monodromy transformations of the RR-felds should acquire anomalous terms, which seem to have a similar origin as the Freed-Witten anomaly for open strings ending on D-branes.

Ref HAL: hal-01160075_v1
Exporter : BibTex | endNote
Résumé:

I'll present the construction of an index in 4d N=2 supersymmetric gauge theories which is smooth across walls of marginal stability and appears as a natural generalization of the CFIV index in two-dimensional theories. I'll explain its physical and geometric interpretation originating in the hyperkahler structure of the 3d theory obtained by compactification on a circle. In the end, I'll also briefly discuss the behavior under wall-crossing of certain generalized theta series which appear, in particular, in the description of NS5-brane instantons in Calabi-Yau compactifications of type II strings.

Ref HAL: hal-01157692_v1
Ref Arxiv: 1406.2360
DOI: 10.1103/PhysRevLett.114.121601
WoS: 000351579000002
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
16 Citations
Résumé:

In theories with $N=2$ supersymmetry on $R^{3,1}$, BPS bound states can decay across walls of marginal stability in the space of Coulomb branch parameters, leading to discontinuities in the BPS indices $\Omega(\gamma,u)$. We consider a supersymmetric index $I$ which receives contributions from 1/2-BPS states, generalizing the familiar Witten index $Tr (-1)^F e^{-\beta H}$. We expect $I$ to be smooth away from loci where massless particles appear, thanks to contributions from the continuum of multi-particle states. Taking inspiration from a similar phenomenon in the hypermultiplet moduli space of $N=2$ string vacua, we conjecture a formula expressing $I$ in terms of the BPS indices $\Omega(\gamma,u)$, which is continuous across the walls and exhibits the expected contributions from single particle states at large $\beta$. This gives a universal prediction for the contributions of multi-particle states to the index $I$. This index is naturally a function on the moduli space after reduction on a circle, closely related to the canonical hyperk\"ahler metric and hyperholomorphic connection on this space.

Commentaires: 7 pages; v2: introduction expanded, minor corrections, differs from published version in PRL in that supplemental material is included as an Appendix. Réf Journal: Phys. Rev. Lett. 114, 121601 (2015)

Ref HAL: hal-01157624_v1
Ref Arxiv: 1412.6057
DOI: 10.1103/PhysRevD.91.064043
WoS: 000351428400006
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
16 Citations
Résumé:

We study the canonical structure of the real first order formulation of general relativity on a null foliation. We use a tetrad decomposition which allows to elegantly encode the nature of the foliation in the norm of a vector in the fibre bundle. The resulting constraint structure shows some peculiarities. In particular, the dynamical Einstein equations propagating the physical degrees of freedom appear in this formalism as second class tertiary constraints, which puts them on the same footing as the Hamiltonian constraint of the Ashtekar's connection formulation. We also provide a framework to address the issue of zero modes in gravity, in particular, to study the non-perturbative fate of the zero modes of the linearized theory. Our results give a new angle on the dynamics of general relativity and can be used to quantize null hypersurfaces in the formalism of loop quantum gravity or spin foams.

Commentaires: 35 pages, 1 figure; minor corrections, added references. Réf Journal: Phys. Rev. D 91, 064043 (2015)