Gravitational blocks: Symplectic covariance unveiled

Abstract

By working in a symplectically covariant real formulation of special Kähler geometry, we propose and give strong evidence for a canonical BPS partition function for AdS×w2M2 near–horizon geometries with arbitrary rotation and generic magnetic and electric charges. Here, M2 is either a two–sphere or a spindle. We also show that how the attractor equations and the Bekenstein–Hawking entropy can be obtained from an extremization principle.