Mathematical Research Letters

Volume 6, Issue 4, July 1999 pp. 429-437.

Four-Manifold Geography and Superconformal Symmetry

Authors: Marcos Mari\~no, Gregory Moore, and Grigor Peradze
Author institution: Yale University

Summary: 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.

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