Four-manifold geography and superconformal symmetry

Details Four-manifold geography and superconformal symmetry Four-manifold geography and superconformal symmetry

1998-12-07

arxiv.org/abs/math/9812042v2

Mathematics

Differential Geometry

9 pages, harvmac b mode, a reference corrected

Scientific paper

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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