Exploring 5d BPS spectra with exponential networks

Banerjee, Sibasish; Longhi, Pietro; Romo, Mauricio

doi:10.1007/s00023-019-00851-x

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学術論文

Exploring 5d BPS spectra with exponential networks

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Banerjee, Sibasish
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s00023-019-00851-x
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arXiv:1811.02875.pdf
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引用

Banerjee, S., Longhi, P., & Romo, M. (2019). Exploring 5d BPS spectra with exponential networks. Annales Henri Poincaré, 20(12), 4055-4162. doi:10.1007/s00023-019-00851-x.

引用: https://hdl.handle.net/21.11116/0000-0005-0C30-8

要旨

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 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. Information about the BPS spectrum is extracted from the geometry of the mirror curve by construction of a nonabelianization map for exponential networks. For the simplest Calabi-Yau, $\mathbb{C}^3$ 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.