2022/09/23 by Nick Dorey, Dorey, Nick, Boan Zhao +1
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.2209.11834
openalex publication_date 2022/09/23 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28
We give a geometric interpretation for superconformal quantum mechanics defined on a hyper-Kahler cone which has an equivariant symplectic resolution. BPS states are identified with certain twisted Dolbeault cohomology classes on the resolved space and their index degeneracies can also be related to the Euler characteristic computed in equivariant sheaf cohomology. In the special case of the Hilbert scheme of K points on C2, we obtain a rigorous estimate for the exponential growth of the index degeneracies of BPS states as K goes to infinity. This growth serves as a toy model for our recently proposed duality between a seven dimensional black hole and superconformal quantum mechanics.