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Exponential Networks for Linear Partitions
by Sibasish Banerjee, Mauricio Romo, Raphael Senghaas, Johannes Walcher
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Submission summary
| Authors (as registered SciPost users): | Johannes Walcher |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2403.14588v3 (pdf) |
| Date submitted: | 2024-10-15 17:52 |
| Submitted by: | Walcher, Johannes |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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 C2⊂C3 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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We thank the authors for taking the time to respond to our comments and questions, and even though we are still not keen on the ordering of section 3 and 4, we think most other comments have been addressed satisfactorily . We do have one remaining question regarding the top paragraph on p4. Could the authors perhaps explain the "local finiteness" in spectral networks vs exponential spectral networks and why this makes the GMN formalism more complicated? (Or perhaps refer to the relevant section in [13].)
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