Papers › BPS Dendroscopy on Local P²
BPS Dendroscopy on Local P²
Pierrick Bousseau, Pierre Descombes, Bruno Le Floch, Boris Pioline
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
The spectrum of BPS states in type IIA string theory compactified on a Calabi-Yau threefold famously jumps across codimension-one walls in complexified K\"ahler moduli space, leading to an intricate chamber structure. The Split Attractor Flow Conjecture posits that the BPS index Ω_z(γ) for given charge γ and moduli z can be reconstructed from the attractor indices Ω_*(γᵢ) counting BPS states of charge γᵢ in their respective attractor chamber, by summing over a finite set of decorated rooted flow trees known as attractor flow trees. If correct, this provides a classification (or dendroscopy) of the BPS spectrum into different topologies of nested BPS bound states, each having a simple chamber structure. Here we investigate this conjecture for the simplest, albeit non-compact, Calabi-Yau threefold, namely the canonical bundle over the projective plane P². Since the K\"ahler moduli space has complex dimension one and the attractor flow preserves the argument of the central charge, attractor flow trees coincide with scattering sequences of rays in a two-dimensional slice of the scattering diagram in the space of stability conditions on the derived category of compactly supported coherent sheaves on K_(P²). We combine previous results on the scattering diagram of K_(P²) in the large volume slice with new results near the orbifold point ℂ³/ℤ₃, and prove that the Split Attractor Flow Conjecture holds true on the physical slice of Π-stability conditions. In particular, while there is an infinite set of initial rays related by the group Γ₁(3) of auto-equivalences, only a finite number of possible decompositions γ=∑ᵢγᵢ contribute to the index Ω_z(γ) for any γ and z, with constituents γᵢ related by spectral flow to the fractional branes at the orbifold point.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections