Infinitely Many M2-instanton Corrections to M-theory on G₂-manifolds

Authors: Andreas P. Braun, Michele Del Zotto, James Halverson, Magdalena Larfors, David R. Morrison and Sakura Schäfer-Nameki

Preprint number: UUITP-06/18

We consider the non-perturbative superpotential for a class of four-dimensional N = 1 vacua obtained from M-theory on seven-manifolds with holonomy G₂. The class of G₂-holonomy manifolds we consider are so-called twisted connected sum (TCS) constructions, which have the topology of a K3-fibration over S³. We show that the non-perturbative superpotential of M-theory on a class of TCS geometries receives infinitely many inequivalent M2-instanton contributions from infinitely many three-spheres, which we conjecture are supersymmetric (and thus associative) cycles. The rationale for our construction is provided by the duality chain of [1], which relates M-theory on TCS G₂-manifolds to E₈×E₈ heterotic backgrounds on the Schoen Calabi-Yau threefold, as well as to F-theory on a K3-fibered Calabi-Yau fourfold. The latter are known to have an infinite number of instanton corrections to the superpotential and it is these contributions that we trace through the duality chain back to the G₂-compactification.