Euler number of Instanton Moduli space and Seiberg-Witten invariants

TL;DR

This paper establishes a connection between the Euler number of instanton moduli spaces and Seiberg-Witten invariants on four-manifolds, providing new insights into topological quantum field theories without relying on duality assumptions.

Contribution

It demonstrates a direct relation between Euler numbers and Seiberg-Witten invariants in topologically twisted N=4 Yang-Mills theory without assuming duality.

Findings

Partition function equals Seiberg-Witten invariants under specific conditions.

Euler number of instanton moduli space relates to Seiberg-Witten invariants.

Derived relations hold without duality assumptions.

Abstract

We show that a partition function of topological twisted N=4 Yang-Mills theory is given by Seiberg-Witten invariants on a Riemannian four manifolds under the condition that the sum of Euler number and signature of the four manifolds vanish. The partition function is the sum of Euler number of instanton moduli space when it is possible to apply the vanishing theorem. And we get a relation of Euler number labeled by the instanton number $k$ with Seiberg-Witten invariants, too. All calculation in this paper is done without assuming duality.