On Seven-Brane Dependent Instanton Prefactors in F-theory

TL;DR

This paper investigates the moduli-dependent prefactors of M5-instanton corrections in F-theory, linking zero modes to seven-branes and analyzing conditions for superpotential zeroes, with implications for moduli stabilization.

Contribution

It provides a method to compute instanton prefactors via zero mode analysis and explores their role in moduli stabilization in F-theory compactifications.

Findings

Prefactor vanishes at E_8 enhancement points.

Many instantons share similar prefactor structures.

Identified conditions for superpotential zeroes related to E_8 points.

Abstract

We study the moduli-dependent prefactor of M5-instanton corrections to the superpotential in four-dimensional F-theory compactifications. In light of the M-theory and type IIb limits and also heterotic duality, we propose that the explicit moduli dependence of the prefactor can be computed by a study of zero modes localized at intersections between the instanton and seven-branes. We present an instanton prefactor in an E_6 F-theory GUT which does not admit a heterotic dual and show that it vanishes if and only if a point of E_8 enhancement is present in the instanton worldvolume. More generically, we discuss the relationship between points of E_8 and superpotential zeroes and give sufficient conditions for such a point to cause a zero, even for an SU(5) GUT. We scan a large class of compactifications for instanton physics and demonstrate that many instantons have the same prefactor structure. We discuss the associated implications and complications for moduli stabilization. We present an explicit resolution and construction of G-flux in a generic E_6 GUT and identify a global compactification of the local model spectral cover which happens to facilitate prefactor computations. Via a Leray spectral sequence, we demonstrate the relationship between right-movers of heterotic worldsheet instantons, 3-3 strings of euclidean D3 instantons, and the Fermi zero modes of M5-instantons.