Instantons in N=2 magnetized D-brane worlds

TL;DR

This paper investigates instanton effects in N=2 super Yang-Mills theories within a string theory framework involving magnetized D-branes, revealing how string amplitudes encode the holomorphic structure of the effective action.

Contribution

It provides a detailed analysis of open string sectors and annulus amplitudes, demonstrating their role in reconstructing the Kahler metric and the holomorphic structure of instanton-induced actions.

Findings

Annulus amplitudes encode Kahler metric factors.

Holomorphic structure of instanton effects is explicitly derived.

Stringy instanton calculus is clarified in magnetized D-brane setups.

Abstract

In a toroidal orbifold of type IIB string theory we study instanton effects in N=2 super Yang-Mills theories engineered with systems of wrapped magnetized D9 branes and Euclidean D5 branes. We analyze the various open string sectors in this brane system and study the 1-loop amplitudes described by annulus diagrams with mixed boundary conditions, explaining their role in the stringy instanton calculus. We show in particular that the non-holomorphic terms in these annulus amplitudes precisely reconstruct the appropriate Kahler metric factors that are needed to write the instanton correlators in terms of purely holomorphic variables. We also explicitly derive the correct holomorphic structure of the instanton induced low energy effective action in the Coulomb branch.