  We propose an explicit formula connecting Donaldson invariants and
Seiberg-Witten invariants of a 4-manifold of simple type via Nekrasov's
deformed partition function for the N=2 SUSY gauge theory with a single
fundamental matter. This formula is derived from Mochizuki's formula, which
makes sense and was proved when the 4-manifold is complex projective. Assuming
our formula is true for a 4-manifold of simple type, we prove Witten's
conjecture and sum rules for Seiberg-Witten invariants (superconformal simple
type condition), conjectured by Mari\~no, Moore and Peradze.

Differential Geometry;High Energy Physics - Theory;Algebraic Geometry