Comments on N=1 Heterotic String Vacua
Abstract
We analyze three aspects of N=1 heterotic string compactifications on elliptically fibered CalabiYau threefolds: stability of vector bundles, fivebrane instanton transitions and chiral matter. First we show that relative FourierMukai transformation preserves absolute stability. This is relevant for vector bundles whose spectral cover is reducible. Then we derive an explicit formula for the number of moduli which occur in (vertical) fivebrane instanton transitions provided a certain vanishing argument applies. Such transitions increase the holonomy of the heterotic vector bundle and cause gauge changing phase transitions. In an Mtheory description the transitions are associated with collisions of bulk fivebranes with one of the boundary fixed planes. In Ftheory they correspond to threebrane instanton transitions. Our derivation relies on an index computation with data localized along the curve which is related to the existence of chiral matter in this class of heterotic vacua. Finally, we show how to compute the number of chiral matter multiplets for this class of vacua allowing to discuss the associated Yukawa couplings.
 Publication:

arXiv eprints
 Pub Date:
 May 2003
 arXiv:
 arXiv:hepth/0305123
 Bibcode:
 2003hep.th....5123A
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Algebraic Geometry
 EPrint:
 33pp, latex2e version, minor modifications, typos corrected