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Exploring 5d BPS Spectra with Exponential Networks

Sibasish Banerjee Max Planck Institute for Mathematics, Vivatsgasse 7, 53111, Bonn, Germany; Riemann center of Geometry and Physics, Leibniz University, Appellstrasse 2, 30167, Hannover, Germany Pietro Longhi Institute for Theoretical Physics, ETH Zurich, 8093, Zurich, Switzerland; Department of Physics and Astronomy, Uppsala University, Box 516 , 75120, Uppsala, Sweden Mauricio Andrés Romo Jorquera School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, 08540, USA; Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China

arXiv subject: High Energy Physics - Theory (hep-th) mathscidoc:2207.74025

Annales Henri Poincaré, 20, 4055–4162, 2019.10
We develop geometric techniques for counting BPS states in five-dimensional gauge theories engineered by M theory on a toric Calabi–Yau threefold. The problem is approached by studying framed 3d–5d wall-crossing in the presence of a single M5 brane wrapping a special Lagrangian submanifold L. The spectrum of 3d–5d BPS states is encoded by the geometry of the manifold of vacua of the 3d–5d system, which further coincides with the mirror curve describing moduli of the Lagrangian brane. The information about the BPS spectrum is extracted from the geometry of the mirror curve by construction of a nonabelianization map for the exponential networks. For the simplest Calabi–Yau, C^3 we reproduce the count of 5d BPS states and match predictions of 3d tt∗ geometry for the count of 3d–5d BPS states. We comment on applications of our construction to the study of enumerative invariants of toric Calabi–Yau threefolds.
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@inproceedings{sibasish2019exploring,
  title={Exploring 5d BPS Spectra with Exponential Networks},
  author={Sibasish Banerjee, Pietro Longhi, and Mauricio Andrés Romo Jorquera},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220706135351738295538},
  booktitle={Annales Henri Poincaré},
  volume={20},
  pages={4055–4162},
  year={2019},
}
Sibasish Banerjee, Pietro Longhi, and Mauricio Andrés Romo Jorquera. Exploring 5d BPS Spectra with Exponential Networks. 2019. Vol. 20. In Annales Henri Poincaré. pp.4055–4162. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220706135351738295538.
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