Accueil >
Production scientifique
|
|
D-instantons, mock modular forms and BPS partition functions
Auteur(s): Alexandrov S.
(Séminaires)
CERN (Geneve, SZ), 2016-10-04
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 to make manifest the modular invariance of the twistorial construction of D-instanton corrected hypermultiplet
moduli space.
|
|
|
D-instantons, mock modular forms and BPS partition functions
Auteur(s): Alexandrov S.
(Séminaires)
Instituto Superior Técnico (Lisbonne, PT), 2016-06-06
Résumé: I will discuss the modular properties of D3-brane instantons appearing in Calabi-Yau string compactifications. I will 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 will show how to construct its modular completion and prove the modular invariance of the twistorial construction of D-instanton corrected hypermultiplet moduli space.
|
|
|
D-instantons, mock modular forms and BPS partition functions
Auteur(s): Alexandrov S.
(Séminaires)
IHES (Bures-sur- Yvette, FR), 2016-05-24
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.
|
|
|
Instantons, wall-crossing and quantum dilogarithm identities
Auteur(s): Alexandrov S.
(Séminaires)
LAPTh (Annecy, FR), 2016-01-29
Résumé: I'll review the phenomenon of wall-crossing in theories with N=2 supersymmetry and its relation to the instanton contributions to the low energy effective actions in gauge and string theories. In the latter case, it is relevant for the description of D-brane instantons. Adding NS5-brane instantons to the story, one arrives to considering certain generalized theta series. I'll derive the properties of these theta series following from the mutual consistency of wall-crossing, D-brane and NS5-brane instantons, and show how these results can be used to get a new type of quantum dilogarithm identities.
|
|
|
Instantons, wall-crossing and quantum dilogarithm identities
Auteur(s): Alexandrov S.
Conférence invité: 2nd French Russian Conference Random Geometry and Physics (Paris, FR, 2016-10-17)
Ref HAL: hal-01386647_v1
Exporter : BibTex | endNote
Résumé: Motivated by mathematical structures appearing in gauge and string theories with N=2 supersymmetry, I’ll consider the behavior of certain generalized theta series under Kontsevich-Soibelman transformations. In Calabi-Yau string vacua, such theta series encode instanton corrections from NS5-branes, and their transformation properties ensure the mutual consistency of NS5-instantons, D-instantons and wallcrossing. It turns out that the transformations are captured by Faddeev’s quantum dilogarithm, and lead to a new type of quantum dilogarithm identities with the quantization parameter inversely proportional to the NS5-brane charge.
|
|
|
Non-perturbative scalar potential inspired by type IIA strings on rigid CY
Auteur(s): Alexandrov S., Ketov Sergei V., Wakimoto Yuki
(Article) Publié:
Journal Of High Energy Physics, vol. p.2016: 66 (2016)
Texte intégral en Openaccess :
Ref HAL: hal-01348152_v1
Ref Arxiv: 1607.05293
DOI: 10.1007/JHEP11(2016)066
WoS: 000387691500005
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
1 Citation
Résumé: Motivated by a class of flux compactifications of type IIA strings on rigid Calabi-Yau manifolds, preserving N=2 local supersymmetry in four dimensions, we derive a non-perturbative potential of all scalar fields from the exact D-instanton corrected metric on the hypermultiplet moduli space. Applying this potential to moduli stabilization, we find a discrete set of exact vacua for axions. At these critical points, the stability problem is decoupled into two subspaces spanned by the axions and the other fields (dilaton and Kähler moduli), respectively. Whereas the stability of the axions is easily achieved, numerical analysis shows instabilities in the second subspace.
|
|
|
Indefinite theta series and generalized error functions
Auteur(s): Alexandrov S., Banerjee S., Manschot Jan, Pioline Boris
(Article) Publié:
Selecta Mathematica (New Series), vol. 24 p.3927-3972 (2018)
Texte intégral en Openaccess :
Ref HAL: hal-01334181_v1
Ref Arxiv: 1606.05495
DOI: 10.1007/s00029-018-0444-9
WoS: WOS:000449794800003
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
7 Citations
Résumé: Theta series for lattices with indefinite signature $(n_+,n_-)$ arise in many areas of mathematics including representation theory and enumerative algebraic geometry. Their modular properties are well understood in the Lorentzian case ($n_+=1$), but have remained obscure when $n_+\geq 2$. Using a higher-dimensional generalization of the usual (complementary) error function, discovered in an independent physics project, we construct the modular completion of a class of `conformal' holomorphic theta series ($n_+=2$). As an application, we determine the modular properties of a generalized Appell-Lerch sum attached to the lattice ${\operatorname A}_2$, which arose in the study of rank 3 vector bundles on $\mathbb{P}^2$. The extension of our method to $n_+>2$ is outlined.
Commentaires: 30 pages, 2 figures
|