Exponential Networks for Linear Partitions
arxiv(2024)
摘要
Previous work has given proof and evidence that BPS states in local
Calabi-Yau 3-folds can be described and counted by exponential networks on the
punctured plane, with the help of a suitable non-abelianization map to the
mirror curve. This provides an appealing elementary depiction of moduli of
special Lagrangian submanifolds, but so far only a handful of examples have
been successfully worked out in detail. In this note, we exhibit an explicit
correspondence between torus fixed points of the Hilbert scheme of points on
ℂ^2⊂ℂ^3 and anomaly free exponential networks attached
to the quadratically framed pair of pants. This description realizes an
interesting, and seemingly novel, "age decomposition" of linear partitions. We
also provide further details about the networks' perspective on the full
D-brane moduli space.
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