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Exponential BPS graphs and D-brane counting on toric Calabi-Yau threefolds: Part II

Sibasish Banerjee Weyertal 86-90, Department of Mathematics, University of Cologne, 50679, Cologne, Germany Pietro Longhi Institute for Theoretical Physics, ETH Zurich, 8093, Zurich, Switzerland Mauricio Andrés Romo Jorquera Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China

Algebraic Geometry arXiv subject: High Energy Physics - Theory (hep-th) mathscidoc:2207.45001

arXiv, 2020.12
We study BPS states of 5d N=1 SU(2) Yang-Mills theory on S^1×R^4. Geometric engineering relates these to enumerative invariants for the local Hirzebruch surface F_0. We illustrate computations of Vafa-Witten invariants via exponential networks, verifying fiber-base symmetry of the spectrum at certain points in moduli space, and matching with mirror descriptions based on quivers and exceptional collections. Albeit infinite, parts of the spectrum organize in families described by simple algebraic equations. Varying the radius of the M-theory circle interpolates smoothly with the spectrum of 4d N=2 Seiberg-Witten theory, recovering spectral networks in the limit.
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@inproceedings{sibasish2020exponential,
  title={Exponential BPS graphs and D-brane counting on toric Calabi-Yau threefolds: Part II},
  author={Sibasish Banerjee, Pietro Longhi, and Mauricio Andrés Romo Jorquera},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220706142443618119543},
  booktitle={arXiv},
  year={2020},
}
Sibasish Banerjee, Pietro Longhi, and Mauricio Andrés Romo Jorquera. Exponential BPS graphs and D-brane counting on toric Calabi-Yau threefolds: Part II. 2020. In arXiv. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220706142443618119543.
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