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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2408.12703 |
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| _version_ | 1866916367387590656 |
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| author | Alim, Murad Bryan, Daniel |
| author_facet | Alim, Murad Bryan, Daniel |
| contents | We propose generating functions which encode the degeneracies and wall-crossing phenomena of $\mathcal{N}=2$ BPS structures. The generating functions have a representation-theoretic origin and are the analogs of the 1/4-BPS dyon counting formula in $\mathcal{N}=4$ theories involving the Weyl denominator formula of a Borcherds-Kac-Moody Lie algebra. A general form of the generating function is suggested based on the Lie algebra associated to the adjacency matrix of the BPS quiver whenever the BPS spectrum of the $\mathcal{N}=2$ theory admits such a description. This proposal is tested for the BPS spectrum of Seiberg-Witten SU(2) theory as well as for the $D6$-$D2$-$D0$ BPS structure of the resolved conifold which are both captured by an affine $A_1$ Lie algebra and are obtained from limits of the $\mathcal{N}=4$ generating function. The general proposal also reproduces the correct BPS spectra and wall-crossing structures for the Argyres-Douglas $A_2$ theory. We further discuss connections to scattering diagrams studied in the context of stability structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12703 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generating functions for $\mathcal{N}=2$ BPS structures Alim, Murad Bryan, Daniel High Energy Physics - Theory 81T30 We propose generating functions which encode the degeneracies and wall-crossing phenomena of $\mathcal{N}=2$ BPS structures. The generating functions have a representation-theoretic origin and are the analogs of the 1/4-BPS dyon counting formula in $\mathcal{N}=4$ theories involving the Weyl denominator formula of a Borcherds-Kac-Moody Lie algebra. A general form of the generating function is suggested based on the Lie algebra associated to the adjacency matrix of the BPS quiver whenever the BPS spectrum of the $\mathcal{N}=2$ theory admits such a description. This proposal is tested for the BPS spectrum of Seiberg-Witten SU(2) theory as well as for the $D6$-$D2$-$D0$ BPS structure of the resolved conifold which are both captured by an affine $A_1$ Lie algebra and are obtained from limits of the $\mathcal{N}=4$ generating function. The general proposal also reproduces the correct BPS spectra and wall-crossing structures for the Argyres-Douglas $A_2$ theory. We further discuss connections to scattering diagrams studied in the context of stability structures. |
| title | Generating functions for $\mathcal{N}=2$ BPS structures |
| topic | High Energy Physics - Theory 81T30 |
| url | https://arxiv.org/abs/2408.12703 |