On Seven-Brane Dependent Instanton Prefactors in F-theory

TL;DR

This work develops a seven-brane perspective on M5-instanton prefactors in F-theory, proposing that the moduli dependence of the instanton prefactor $A(oldsymbol{phi})$ is governed by the cohomology of a line bundle on a local spectral curve $c_{ ext{loc}}$ and can be computed without a heterotic dual. The authors connect this local computation to M5-brane physics via the chiral 2-form theta-divisor on the intermediate Jacobian ${\,\mathcal J}(M5)$ and to heterotic data when a dual exists, using a compact realization of ${\cal C}_{ ext{loc}}$ and a fiberwise cylinder map. They perform a large Kreuzer–Skarke scan for $G_{4d}=E_6$ to classify instanton prefactors, uncovering a small set of universal structures and highlighting two especially interesting loci: zeros coinciding with points of $E_8$ enhancement, and cases where the prefactor vanishes identically. The paper also presents three illustrative examples, including a heterotic-dual case and two intrinsic F-theory cases, one of which demonstrates an identically vanishing prefactor, underscoring the intricate dependence of nonperturbative effects on seven-brane moduli and the potential impact on moduli stabilization. Overall, the work provides a concrete, computationally accessible framework for determining seven-brane dependent instanton prefactors and clarifies their geometric and duality structures. It advances understanding of nonperturbative effects in F-theory GUTs and offers practical tools for global model building and moduli stabilization analyses in string phenomenology.

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.