On Mathieu moonshine and Gromov-Witten invariants

Andreas Banlaki (Institut für Theoretische Physik, TU Wien, Wiedner Hauptstraße 8-10, Vienna, A-1040, Austria) ; Abhishek Chowdhury (Institut für Theoretische Physik, TU Wien, Wiedner Hauptstraße 8-10, Vienna, A-1040, Austria; IIT Bhubaneshwar, SBS Building, Argul, Khordha, Odisha, 752050, India) ; Abhiram Kidambi (Institut für Theoretische Physik, TU Wien, Wiedner Hauptstraße 8-10, Vienna, A-1040, Austria) ; Maria Schimpf (Institut für Theoretische Physik, TU Wien, Wiedner Hauptstraße 8-10, Vienna, A-1040, Austria)

We provide further evidence that CY 3 manifolds are involved in an intricate way in Mathieu moonshine, i.e., their Gromov-Witten invariants are related to the expansion coefficients of the twined/twisted-twined elliptic genera of K3. We use the string duality between CHL orbifolds of heterotic string theory on K3 × T 2 and type IIA string theory on CY 3 manifolds to explicitly show this connection. We then work out two concrete examples where we exactly match the expansion coefficients on both sides of the duality.

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      "value": "We provide further evidence that CY 3 manifolds are involved in an intricate way in Mathieu moonshine, i.e., their Gromov-Witten invariants are related to the expansion coefficients of the twined/twisted-twined elliptic genera of K3. We use the string duality between CHL orbifolds of heterotic string theory on K3 \u00d7 T 2 and type IIA string theory on CY 3 manifolds to explicitly show this connection. We then work out two concrete examples where we exactly match the expansion coefficients on both sides of the duality."
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Published on:
14 February 2020
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2020 (2020)
Issue 2
Pages 1-26
DOI:
https://doi.org/10.1007/JHEP02(2020)082
arXiv:
1811.11619
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: