New Issues in Manifolds of Su(3) Holonomy

Abstract

It is shown that in compactification of superstrings on manifolds of SU(3) holonomy, the superpotential receives no string theoretic corrections from the form it takes in the field theoretic limit, at least to all finite orders in sigma model perturbation theory. Modulo nonperturbative effects, this implies that those manifolds do indeed obey the exact classical equations of super-string theory, as has been argued on other grounds. Also, it is pointed out that the superpotential – even in the field theory limit – contains terms coupling charged fields to E 6 singlets as well as self-couplings of the charged fields. A slightly tentative argument is given that on certain manifolds of SU(3) holonomy – though not all – it is possible to find conformally invariant sigma models that, while keeping unbroken supersymmetry, break E 8 to SO(10) or SU(5) rather than E 6 . Including the effects of Wilson lines this would mean that E 8 could be broken precisely to SU(3) × SU(2) × U(1) while keeping unbroken supersymmetry. These facts may open avenues for solving the problems associated with neutrino masses, proton decay, and renormalization group calculations of coupling constants. They also may lead to models with fewer unknown parameters than have been present in previous quasi-realistic models.