Massless spectra of three generation U(N) heterotic string vacua - Blumenhagen, Ralph; Weigand, Timo (Journal of high energy physics, 2007)
We provide the methods to compute the complete massless spectra of a class of recently introduced supersymmetric E 8 × E 8 heterotic string models which invoke vector bundles with U( N ) structure group on simply connected Calabi-Yau manifolds and which yield flipped SU(5) and MSSM string vacua of potential phenomenological interest. We apply Leray spectral sequences in order to derive the localisation of the cohomology groups H i ( X, V a ⊗ V b ), H i ( X, ##IMG## [http://ej.iop.org/icons/Entities/bigwedge.gif] bigwedge 2 V ) and H i ( X, S 2 V ) for vector bundles defined via Fourier-Mukai transforms on elliptically fibered Calabi-Yau manifolds. By the method of bundle extensions we define a stable U(4) vector bundle leading to the first flipped SU(5) model with just three generations, i.e. without any vector-like matter. Along the way, we propose the notion of λ-stability for heterotic bundles.