Superconformal invariance and the geography of four-manifolds

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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59 pages, harvmac b mode, four figures, some clarifications and references added

Scientific paper

10.1007/s002200050694

The correlation functions of supersymmetric gauge theories on a four-manifold X can sometimes be expressed in terms of topological invariants of X. We show how the existence of superconformal fixed points in the gauge theory can provide nontrivial information about four-manifold topology. In particular, in the example of gauge group SU(2) with one doublet hypermultiplet, we derive a theorem relating classical topological invariants such as the Euler character and signature to sum rules for Seiberg-Witten invariants.

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