Mathematical Research Letters
Volume 6 (1999)
Four-Manifold Geography and Superconformal Symmetry
Pages: 429 – 437
A compact oriented 4-manifold is defined to be of “superconformal simple type” if certain polynomials in the basic classes (constructed using the Seiberg-Witten invariants) vanish identically. We show that all known 4-manifolds of $b_2^+ >1$ are of superconformal simple type, and that the numerical invariants of 4-manifolds of superconformal simple type satisfy a generalization of the Noether inequality. We sketch how these phenomena are predicted by the existence of certain four-dimensional superconformal quantum field theories.