The Decay and Fission algorithm for good quivers

Let QQ be a good 3d N=4\mathcal{N}=4 quiver theory, let MC(Q)\mathcal{M}_C(Q) denote its Coulomb branch, and let L\mathcal{L} be the set of decay and fission products of QQ, ordered by \succcurlyeq. The Decay and Fission algorithm. There exists a 1-to-1 correspondence between the poset of symplectic leaves of MC(Q)\mathcal{M}_C(Q) and the poset (L,)(\mathcal{L},\succcurlyeq). This conjectural correspondence would give a combinatorial construction of the Hasse diagram of the Coulomb branch. Its general validity is presented as conjectural in the source.

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Primary source

Antoine Bourget, Quentin Lamouret, Sinan Moura Soysüren and Marcus Sperling, “Classifying Isolated Symplectic Singularities via 3d N=4 Coulomb Branches”, arXiv:2504.05373 (2026).

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