Attractor invariants for the local second del Pezzo phase

At least 5 years old · documented by

Let QQ be the quiver for the local phase labelled PdP2\mathrm{PdP}_2, let eie_i be its vertex dimension vectors, and let d\mathrm{d} be the dimension vector of a single D0-brane. Local PdP2\mathrm{PdP}_2 attractor conjecture. For every vertex ii, Ω∗(ei)=1\Omega_*(e_i)=1, and for every n≥1n\geq1, Ω∗(nd)=−y−1(y4+3y2+1)\Omega_*(n\mathrm{d})=-y^{-1}(y^4+3y^2+1); for every n≥0n\geq0, Ω∗(e1+e3+nd)=Ω∗(e2+e4+e5+nd)=−y\Omega_*(e_1+e_3+n\mathrm{d})=\Omega_*(e_2+e_4+e_5+n\mathrm{d})=-y; all other attractor invariants vanish. The formula was verified in small degrees and records additional non-simple attractor states in this phase; the source gives no general proof.

References

Primary source

Sergey Mozgovoy and Boris Pioline, “Attractor invariants, brane tilings and crystals”, arXiv:2012.14358 (2022).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.