On the instanton contributions to the masses and couplings of E_{6} singlets
Abstract
We consider the gauge neutral matter in the lowenergy effective action for string theory compactification on a CalabiYau manifold with (2,2) worldsheet supersymmetry. At the classical level these states (the 1's of E_{6}) correspond to the cohomology group H ^{1}( 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 Kähler parameters t_{i} through factors of the form e^{2 πit}_{i} and also depend on the complex structure parameters. For simplicity we consider in greatest detail the quintic threefold P_{4}[5]. It follows on general grounds that the total mass is often, and perhaps always, zero. The contribution of individual instantons is however nonzero 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 CalabiYau 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 1^{3} and neutral and charged fields 27 · overline27 · 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 firstorder worldsheet instanton correction to these couplings and argue that these also vanish.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1995
 DOI:
 10.1016/05503213(95)00403F
 arXiv:
 arXiv:hepth/9505164
 Bibcode:
 1995NuPhB.454..127B
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Algebraic Geometry
 EPrint:
 40 pages, plain TeX with epsf, one uuencoded figure