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Topological recursion and mirror curves

Bouchard, Vincent and Sułkowski, Piotr (2012) Topological recursion and mirror curves. Advances in Theoretical and Mathematical Physics, 16 (5). pp. 1443-1483. ISSN 1095-0761. https://resolver.caltech.edu/CaltechAUTHORS:20130730-104457265

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Abstract

We study the constant contributions to the free energies obtained through the topological recursion applied to the complex curves mirror to toric Calabi–Yau threefolds. We show that the recursion reproduces precisely the corresponding Gromov–Witten invariants, which can be encoded in powers of the MacMahon function. As a result, we extend the scope of the “remodeling conjecture” to the full free energies, including the constant contributions. In the process, we study how the pair of pants decomposition of the mirror curves plays an important role in the topological recursion. We also show that the free energies are not, strictly speaking, symplectic invariants, and that the recursive construction of the free energies does not commute with certain limits of mirror curves.


Item Type:Article
Related URLs:
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http://intlpress.com/site/pub/pages/journals/items/atmp/content/vols/0016/0005/00026471/index.htmlPublisherArticle
http://arxiv.org/abs/1105.2052arXivArticle
Additional Information:© 2012 International Press. We would like to thank Cedric Berndt, Bertrand Eynard, Sergei Gukov, Amir Kashani–Poor and Olivier Marchal for enjoyable discussions. The research of V.B. is supported by a University of Alberta startup grant and an NSERC Discovery grant. The research of P.S. is supported by the DOE grant DE-FG03-92ER40701FG-02 and the European Commission under the Marie-Curie International Outgoing Fellowship Programme.
Funders:
Funding AgencyGrant Number
University of Alberta startup grantUNSPECIFIED
NSERC Discovery grantUNSPECIFIED
Department of Energy (DOE)DE-FG03-92ER40701FG-02
European Commission Marie-Curie International Outgoing Fellowship ProgrammeUNSPECIFIED
Issue or Number:5
Record Number:CaltechAUTHORS:20130730-104457265
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20130730-104457265
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:39651
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:31 Jul 2013 14:40
Last Modified:03 Oct 2019 05:09

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