F Theory on K3xK3 and Instantons on 7-branes

TL;DR

This paper explores N=2 supersymmetric compactifications in F-theory and heterotic theory, focusing on vector bundles, moduli space transitions, and anomaly cancellation in K3xK3 compactifications.

Contribution

It provides a detailed analysis of the heterotic-F-theory correspondence, vector bundle spectral theory, and instanton moduli space transitions in K3xK3 compactifications.

Findings

Spectral theory for vector bundles on K3xT^2 elucidated.

Heterotic-F-theory map clarified for specific compactifications.

Transitions between moduli space branches described in detail.

Abstract

We discuss N=2 supersymmetric compactifications to four dimensions from the point of view of F-theory and heterotic theory. In a relatively simple setup, we illustrate the spectral theory for vector bundles on K3xT^2 and discuss the heterotic -- F-theory map. The moduli space of instantons on the 7-brane wrapped around K3 is discussed from the point of view of Higgs mechanism in the effective four-dimensional N=2 theory. This allows us to elaborate on the transitions between various branches of the moduli space of the heterotic/F-theory. We also describe the F-theory compactification on smooth K3xK3 without the 3-branes in which the anomaly is cancelled by the gauge fields.