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Partition Functions of \(\mathcal{N}=(2,2)\) Supersymmetric Sigma Models and Special Geometry on the Moduli Spaces of Calabi-Yau Manifolds

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Abstract

We study a new example of a mirror relation between the exact partition functions of \(\mathcal{N}=(2,2)\) super-symmetric gauged linear sigma models on the sphere S2 and the special Kähler geometry on the moduli spaces of Calabi-Yau manifolds. Using exact calculations, we show this relation indeed holds for Calabi-Yau manifolds of the Berglund-Hubsch type with two moduli.

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Acknowledgments

The authors are grateful to K. Aleshkin, G. Koshevoi, F. Malikov, A. Litvinov, V. Pestun, and M. Kontsevich for the useful discussions.

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Authors and Affiliations

  1. Landau Institute for Theoretical Physics, RAS, Chernogolovka, Moscow Oblast, Russia

    A. A. Belavin & B. A. Eremin

  2. Kharkevich Institute for Information Transmission Problems, Moscow, Russia

    A. A. Belavin

  3. Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Oblast, Russia

    B. A. Eremin

Authors
  1. A. A. Belavin
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  2. B. A. Eremin
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Correspondence to A. A. Belavin.

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Conflicts of interest. The authors declare no conflicts of interest.

Additional information

This research was performed at the Landau Institute for Theoretical Physics and was supported by a grant from the Russian Science Foundation (Project No. 18-12-00439).

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 201, No. 2, pp. 222–231, November, 2019.

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Belavin, A.A., Eremin, B.A. Partition Functions of \(\mathcal{N}=(2,2)\) Supersymmetric Sigma Models and Special Geometry on the Moduli Spaces of Calabi-Yau Manifolds. Theor Math Phys 201, 1606–1613 (2019). https://doi.org/10.1134/S0040577919110060

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  • DOI: https://doi.org/10.1134/S0040577919110060

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