From Seiberg-Witten invariants to topological Green-Schwarz string

TL;DR

This paper explores the connection between Seiberg-Witten invariants and Gromov-Witten invariants in 4-manifolds, proposing that their equivalence is governed by the N=2 Green-Schwarz string theory.

Contribution

It establishes a physical framework linking Seiberg-Witten invariants to Gromov-Witten invariants via the Green-Schwarz string, providing new insights into topological invariants.

Findings

Seiberg-Witten invariants are equivalent to certain Gromov-Witten invariants.

The pseudo-holomorphic curves are governed by the N=2 Green-Schwarz string.

Proposes a physical interpretation of topological invariants in string theory.

Abstract

In this note we describe the physics of equivalence of the Seiberg-Witten invariants of 4-manifolds and certain Gromov-Witten invariants defined by pseudo-holomorphic curves. We show that physics of the pseudo-holomorphic curves should be governed by the N=2 Green-Schwarz string.