Stability of vector bundles from F-theory

TL;DR

This paper explores the stability conditions of holomorphic vector bundles on elliptically fibered Calabi-Yau manifolds within F-theory, using toric geometry to relate stability to the existence of specific holomorphic sections.

Contribution

It introduces a toric geometric framework to analyze stability of vector bundles in F-theory, linking stability criteria to holomorphic sections of line bundles.

Findings

Stability conditions are expressed via holomorphic sections.

A toric map relates F-theory and heterotic duality.

The approach provides a geometric criterion for bundle stability.

Abstract

We use a recently proposed formulation of stable holomorphic vector bundles $V$ on elliptically fibered Calabi--Yau n-fold $Z_n$ in terms of toric geometry to describe stability conditions on $V$. Using the toric map $f: W_{n+1} \to (V,Z_n)$ that identifies dual pairs of F-theory/heterotic duality we show how stability can be related to the existence of holomorphic sections of a certain line bundle that is part of the toric construction.