On the instanton contributions to the masses and couplings of E6 singlets

Abstract We consider the gauge neutral matter in the low-energy effective action for string theory compactification on a Calabi-Yau manifold with (2,2) world-sheet supersymmetry. At the classical level these states (the 1's of E6) correspond to the cohomology group H1( M , End T). We examine the first order contribution of instantons to the mass matrix of these particles. In principle, these corrections depend on the Kahler parameters ti through factors of the form e2πiti and also depend on the complex structure parameters. For simplicity we consider in greatest detail the quintic threefold P4[5]. It follows on general grounds that the total mass is often, and perhaps always, zero. The contribution of individual instantons is however non-zero and the contribution of a given instanton may develop poles associated with instantons coalescing for certain values of the complex structure. This can happen when the underlying Calabi-Yau manifold is smooth. Hence these poles must cancel between the coalescing instantons in order that the superpotential be finite. We examine also the Yukawa couplings involving neutral matter 13 and neutral and charged fields 27 · 27 · 1 , which have been little investigated even though they are of phenomenological interest. We study the general conditions under which these couplings vanish classically. We also calculate the first-order world-sheet instanton correction to these couplings and argue that these also vanish.