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Exponential BPS Graphs and D Brane Counting on Toric Calabi-Yau Threefolds: Part I

Sibasish Banerjee Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093, Warsaw, Poland Pietro Longhi Institute for Theoretical Physics, ETH Zurich, 8093, Zurich, Switzerland; Mathematical Sciences Research Institute, 17 Gauss Way, Berkeley, CA, 94720, USA Mauricio Andrés Romo Jorquera Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China

arXiv subject: High Energy Physics - Theory (hep-th) mathscidoc:2207.74027

Communications in Mathematical Physics, 388, 893–945, 2021.10
We study BPS spectra of D-branes on local Calabi-Yau threefolds O(−p)⊕O(p−2)→P^1 with p=0,1, corresponding to C^3/Z_2 and the resolved conifold. Nonabelianization for exponential networks is applied to compute directly unframed BPS indices counting states with D2 and D0 brane charges. Known results on these BPS spectra are correctly reproduced by computing new types of BPS invariants of 3d-5d BPS states, encoded by nonabelianization, through their wall-crossing. We also develop the notion of exponential BPS graphs for the simplest toric examples, and show that they encode both the quiver and the potential associated to the Calabi-Yau via geometric engineering.
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@inproceedings{sibasish2021exponential,
  title={Exponential BPS Graphs and D Brane Counting on Toric Calabi-Yau Threefolds: Part I},
  author={Sibasish Banerjee, Pietro Longhi, and Mauricio Andrés Romo Jorquera},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220706140256817788540},
  booktitle={Communications in Mathematical Physics},
  volume={388},
  pages={893–945},
  year={2021},
}
Sibasish Banerjee, Pietro Longhi, and Mauricio Andrés Romo Jorquera. Exponential BPS Graphs and D Brane Counting on Toric Calabi-Yau Threefolds: Part I. 2021. Vol. 388. In Communications in Mathematical Physics. pp.893–945. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220706140256817788540.
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