Ref HAL: hal-01330956_v1
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Résumé:

I'll discuss the modular properties of D3-brane instantons appearing in Calabi-Yau string compactifications. I'll show that the D3-instanton contribution to a certain geometric potential on the hypermultiplet moduli space can be related to the elliptic genus of (0,4) SCFT. The modular properties of the potential imply that the elliptic genus associated with non-primitive divisors of Calabi-Yau is only mock modular. I'll show how to construct its modular completion and prove the modular invariance of the twistorial construction of D-instanton corrected hypermultiplet moduli space.

Ref HAL: cea-01318414_v1
Ref Arxiv: 1605.05945
DOI: 10.1007/s00220
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
Résumé:

We study D3-instanton corrections to the hypermultiplet moduli space in type IIB string theory compactified on a Calabi-Yau threefold. In a previous work, consistency of D3-instantons with S-duality was established at first order in the instanton expansion, using the modular properties of the M5-brane elliptic genus. We extend this analysis to the two-instanton level, where wall-crossing phenomena start playing a role. We focus on the contact potential, an analogue of the Kähler potential which must transform as a modular form under S-duality. We show that it can be expressed in terms of a suitable modification of the partition function of D4-D2-D0 BPS black holes, constructed out of the generating function of MSW invariants (the latter coincide with Donaldson-Thomas invariants in a particular chamber). Modular invariance of the contact potential then requires that, in case where the D3-brane wraps a reducible divisor, the generating function of MSW invariants must transform as a vector-valued mock modular form, with a specific modular completion built from the MSW invariants of the constituents. Physically, this gives a powerful constraint on the degeneracies of BPS black holes. Mathematically, our result gives a universal prediction for the modular properties of Donaldson-Thomas invariants of pure two-dimensional sheaves.

Commentaires: 33 pages

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.