Generating functions for $\mathcal{N}=2$ BPS structures
| Autor: | Alim, Murad, Bryan, Daniel |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 73 pages, 8 figures |
| Databáze: | arXiv |
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