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April 15, 2026Annales Henri PoincaréOpen Access

BPS Dendroscopy on Local P¹ P¹

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Authors

BFBruno Le FlochCentre National de la Recherche ScientifiqueBPBoris PiolineRRRishi RajCentre National de la Recherche Scientifique

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Implication

This work analyzes BPS states in a non-compact toric Calabi-Yau geometry, revealing stability characteristics and flow structures.

Key Points

  • The aim is to study the scattering diagram of BPS states associated with local P1 times P1, focusing on moduli-dependent structures.
  • Constructed scattering diagrams for the quiver near the orbifold point and the large volume slice.
  • Analyzed the physical slice of Π-stability conditions with a Z^4 action related to the modular group.
  • Explored the implications for the split attractor flow tree conjecture in this context.
  • The scattering diagram clarifies the organization of BPS indices based on attractor indices.
  • Insights from simple limits support the construction of the full scattering diagram.
  • The example further validates previous studies on local P2 with added complexity from mass parameters.

Cite This Study

Floch et al. (2026) studied this question.

synapsesocial.com/papers/69df2ba0e4eeef8a2a6b0918https://doi.org/10.1007/s00023-026-01666-3
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