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D-instantons in Type II string theory on Calabi-Yau threefolds
Auteur(s): Alexandrov S.
Conférence invité: Workshop on Black Holes, BPS and Quantum Information (Lisbonne (on line), PT, 2021-09-20)
Texte intégral en Openaccess :
Ref HAL: hal-03355857_v1
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Résumé: Euclidean D-branes wrapped on non-trivial cycles of a Calabi-Yau threefold are known to affect the metric on the hypermultiplet moduli space determining the effective action of type II strings on such manifolds. After reviewing the existing results on the instanton corrected metric following from a combination of constraints imposed by supersymmetry and dualities, I'll show how the D-instanton effects can be computed by a direct worldsheet approach. It required solving several conceptual and technical problems and can now be extended to compactifications with lower supersymmetry.The talk is based on joint work with A. Sen and B. Stefanski.
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D-instantons in Type IIA string theory on Calabi-Yau threefolds
Auteur(s): Alexandrov S., Sen Ashoke, Stefański Bogdan
(Article) Publié:
Journal Of High Energy Physics, vol. 2021 p.18 (2021)
Texte intégral en Openaccess :
Ref HAL: hal-03319142_v1
Ref Arxiv: 2108.04265
DOI: 10.1007/JHEP11(2021)018
Ref. & Cit.: NASA ADS
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Résumé: Type IIA string theory compactified on a Calabi-Yau threefold has a hypermultiplet moduli space whose metric is known to receive non-perturbative corrections from Euclidean D2-branes wrapped on 3-cycles. These corrections have been computed earlier by making use of mirror symmetry, S-duality and twistorial description of quaternionic geometries. In this paper we compute the leading corrections in each homology class using a direct world-sheet approach without relying on any duality symmetry or supersymmetry. Our results are in perfect agreement with the earlier predictions.
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Conformal TBA for resolved conifolds
Auteur(s): Alexandrov S., Pioline Boris
(Article) Publié:
Annales De L'insitut Henri Poincare (A) Theoretical Physics, vol. 23 p.1909–1949 (2022)
Texte intégral en Openaccess :
Ref HAL: hal-03271316_v1
Ref Arxiv: 2106.12006
DOI: 10.1007/s00023-021-01129-x
WoS: 000722791700001
Ref. & Cit.: NASA ADS
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1 Citation
Résumé: We revisit the Riemann-Hilbert problem determined by Donaldson-Thomas invariants for the resolved conifold and for other small crepant resolutions. While this problem can be recast as a system of TBA-type equations in the conformal limit, solutions are ill-defined due to divergences in the sum over infinite trajectories in the spectrum of D2-D0-brane bound states. We explore various prescriptions to make the sum well-defined, show that one of them reproduces the existing solution in the literature, and identify an alternative solution which is better behaved in a certain limit. Furthermore, we show that a suitable asymptotic expansion of the $\tau$ function reproduces the genus expansion of the topological string partition function for any small crepant resolution. As a by-product, we conjecture a new integral representation for the double sine function.
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Heavenly metrics, BPS indices and twistors
Auteur(s): Alexandrov S., Pioline Boris
(Article) Publié:
Letters In Mathematical Physics, vol. 111 p.116 (2021)
Texte intégral en Openaccess :
Ref HAL: hal-03206137_v1
Ref Arxiv: 2104.10540
DOI: 10.1007/s11005-021-01455-5
Ref. & Cit.: NASA ADS
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Résumé: Recently T. Bridgeland defined a complex hyperk\"ahler metric on the tangent bundle over the space of stability conditions of a triangulated category, based on a Riemann-Hilbert problem determined by the Donaldson-Thomas invariants. This metric is encoded in a function $W(z,\theta)$ satisfying a heavenly equation, or a potential $F(z,\theta)$ satisfying an isomonodromy equation. After recasting the RH problem into a system of TBA-type equations, we obtain integral expressions for both $W$ and $F$ in terms of solutions of that system. These expressions are recognized as conformal limits of the `instanton generating potential' and `contact potential' appearing in studies of D-instantons and BPS black holes. By solving the TBA equations iteratively, we reproduce Joyce's original construction of $F$ as a formal series in the rational DT invariants. Furthermore, we produce similar solutions to deformed versions of the heavenly and isomonodromy equations involving a non-commutative star-product. In the case of a finite uncoupled BPS structure, we rederive the results previously obtained by Bridgeland and obtain the so-called $\tau$ function for arbitrary values of the fiber coordinates $\theta$, in terms of a suitable two-variable generalization of Barnes' $G$ function.
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Canonical structure of minimal varying $\Lambda$ theories
Auteur(s): Alexandrov S., Speziale Simone, Zlosnik Tom
(Article) Publié:
Classical And Quantum Gravity, vol. 38 p.175011 (2021)
Texte intégral en Openaccess :
Ref HAL: hal-03197323_v1
Ref Arxiv: 2104.03753
DOI: 10.1088/1361-6382/ac1852
Ref. & Cit.: NASA ADS
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Résumé: Minimal varying $\Lambda$ theories are defined by an action built from the Einstein-Cartan-Holst first order action for gravity with the cosmological constant $\Lambda$ as an independent scalar field, and supplemented by the Euler and Pontryagin densities multiplied by $1/\Lambda$. We identify the canonical structure of these theories which turn out to represent an example of irregular systems. We find five degrees of freedom on generic backgrounds and for generic values of parameters, whereas if the parameters satisfy a certain condition (which includes the most commonly considered Euler case) only three degrees of freedom remain. On de Sitter-like backgrounds the canonical structure changes, and due to an emergent conformal symmetry one degree of freedom drops from the spectrum. We also analyze the self-dual case with an holomorphic action depending only on the self-dual part of the connection. In this case we find two (complex) degrees of freedom, and further discuss the Kodama state, the restriction to de Sitter background and the effect of reality conditions.
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Mock modularity and refinement: from BPS black holes to Vafa-Witten theory
Auteur(s): Alexandrov S.
Conférence invité: Workshop on Black Holes: BPS, BMS and Integrability. (Lisbonne, PT, 2020-09-07)
Ref HAL: hal-02986300_v1
Exporter : BibTex | endNote
Résumé: The generating functions of degeneracies of D4-D2-D0 black holes in Type IIstring compactifications on Calabi-Yau threefolds are examples of (higher depth) mock modular forms. I'll explain how S-duality can be used to derive an explicit form for their modular completions, which becomes particularly simple in the presence of a refinement. This result turns out to have many applications going beyond the original context. In particular, I'll show that it can be usedi) to reproduce and generalize in an easy way the known results on modular properties of the generating functions of BPS dyons in N=4 string compactifications;ii) to find Vafa-Witten invariants of arbitrary(!) rank on CP^2, Hirzebruch and del Pezzo surfaces; iii) to obtain holomorphic anomaly equations for BPS partition functions;iv) to reveal a non-commutative structure induced by the refinement on the moduli space of compactified theory.
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Refinement and modularity of immortal dyons
Auteur(s): Alexandrov S., Nampuri Suresh
(Article) Publié:
Journal Of High Energy Physics, vol. 2021 p.147 (2021)
Texte intégral en Openaccess :
Ref HAL: hal-02930775_v1
Ref Arxiv: 2009.01172
DOI: 10.1007/JHEP01(2021)147
Ref. & Cit.: NASA ADS
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Résumé: Extending recent results in ${\cal N}=2$ string compactifications, we propose that the holomorphic anomaly equation satisfied by the modular completions of the generating functions of refined BPS indices has a universal structure independent of the number ${\cal N}$ of supersymmetries. We show that this equation allows to recover all known results about modularity (under $SL(2,\mathbb{Z})$ duality group) of BPS states in ${\cal N}=4$ string theory. In particular, we reproduce the holomorphic anomaly characterizing the mock modular behavior of quarter-BPS dyons and generalize it to the case of non-trivial torsion invariant.
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