A Note On Zeroes Of Superpotentials In F-Theory

TL;DR

This paper examines how superpotential terms in 4D F-theory depend on moduli, identifying conditions under which these terms vanish due to brane positions and 2-form VEVs, with implications for moduli stabilization.

Contribution

It provides an alternative derivation of superpotential zeros in F-theory related to brane positions and 2-form VEVs, extending previous M-theory results.

Findings

Superpotential vanishes when 3-brane hits the divisor.

Zero occurs for specific 2-form VEVs with non-trivial 3-cycles.

Alternative derivation for F-theory case provided.

Abstract

We discuss the dependence of superpotential terms in 4D F-theory on moduli parameters. Two cases are studied: the dependence on world-filling 3-brane positions and the dependence on 2-form VEVs. In the first case there is a zero when the 3-brane hits the divisor responsible for the superpotential. In the second case, which has been extensively discussed by Witten in 3D M-theory, there is a zero for special values of 2-form VEVs when the M-theory divisor contains non-trivial 3-cycles. We give an alternative derivation of this fact for the special case of F-theory.