Fluxed M5-instantons in F-theory
Max Kerstan, Timo Weigand
TL;DR
This work analyzes non-perturbative superpotential contributions from M5-instantons in F-theory on elliptically fibered Calabi–Yau fourfolds, focusing on vertical divisors and the chiral 2-form on the M5, and develops a holomorphic factorisation framework to compute the M5 partition function. By explicitly matching the M5 flux sum with the fluxed Euclidean D3-instanton partition function in Type IIB, the authors fix the canonical M5 partition function (including the choice of theta-function sector) and establish precise identifications between M5 and E3 flux data. They then incorporate G4-flux effects, showing that a nonvanishing pullback iota^*G4 induces M2-brane states ending on the M5 and yields selection rules for charged zero modes that reproduce Type IIB chiral indices and U(1) charges, including massive U(1) effects. The analysis is illustrated in a global SU(5) × U(1) model, where explicit integrals over matter surfaces and U(1)-related surfaces demonstrate the equivalence of F-theory and Type IIB selection rules. The results advance understanding of non-perturbative dynamics in F-theory and provide a framework for moduli stabilisation scenarios involving M5-instantons, while highlighting directions for extending to non-rigid divisors and non-harmonic fluxes.
Abstract
We analyse the non-perturbative superpotential due to M5-brane instantons in F-theory compactifications on Calabi-Yau fourfolds. The M5 partition function is obtained via holomorphic factorisation by explicitly performing the sum over chiral 3-form fluxes. Comparison with the partition function of fluxed Euclidean D3-brane instantons in Type IIB orientifolds allows us to fix the spin structure on the intermediate Jacobian of the M5-instanton. We furthermore analyse the contribution of the M5-instanton to the superpotential in the presence of G4 gauge flux, where the superpotential is dressed with matter fields. We explicitly evaluate the pullback of G4 onto the M5-brane as a measure for the presence of charged instanton zero modes. This accounts for the M5 charge both under massless U(1)s, if present, and under what corresponds in Type II language to geometrically massive U(1)s.