Superconformal invariance and the geography of four-manifolds

TL;DR

This paper explores how superconformal fixed points in supersymmetric gauge theories yield new insights into four-manifold topology, linking classical invariants with Seiberg-Witten invariants through theoretical analysis.

Contribution

It demonstrates how superconformal invariance can be used to derive relations between classical topological invariants and Seiberg-Witten invariants for four-manifolds.

Findings

Derived a theorem relating Euler character and signature to Seiberg-Witten invariants.

Showed how superconformal fixed points inform four-manifold topology.

Connected gauge theory correlation functions to topological invariants.

Abstract

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.