On Four-Dimensional Compactifications of F-Theory

TL;DR

This paper explores the moduli space of four-dimensional F-theory compactifications, describing transitions via 3-brane-instantons, and maps these to heterotic string theory, revealing a web structure in the moduli space.

Contribution

It provides a dual heterotic description of F-theory moduli space transitions and maps complex structure and bundle data between the theories.

Findings

Transition between moduli space branches involves 3-brane-instantons.

A dual heterotic picture of F-theory transitions is established.

The moduli space exhibits a web structure similar to that of semi-stable bundles on CY_3.

Abstract

Branches of moduli space of F-theory in four dimensions are investigated. The transition between two branches is described as a 3-brane-instanton transition on a 7-brane. A dual heterotic picture of the transition is presented and the F-theory - heterotic theory map is given. The F-theory data - complex structure of the Calabi-Yau fourfold and the instanton bundle on the 7-brane is mapped to the heterotic bundle on the elliptic Calabi-Yau threefold CY_3. The full moduli space has a web structure which is also found in the moduli space of semi-stable bundles on $CY_3$. Matter content of the four-dimensional theory is discussed in both F-theory and heterotic theory descriptions.