Massless spectra of three generation U(N) heterotic string vacua

We provide the methods to compute the complete massless spectra of a class ofrecently introduced supersymmetric E8 x E8 heterotic string models which invokevector bundles with U(N) structure group on simply connected Calabi-Yaumanifolds and which yield flipped SU(5) and MSSM string vacua of potentialphenomenological interest. We apply Leray spectral sequences in order to derivethe localisation of the cohomology groups H^i(X,V_a \times V_b),H^i(X,\bigwedge^2 V) and H^i(X,{\bf S}^2 V) for vector bundles defined viaFourier-Mukai transforms on elliptically fibered Calabi-Yau manifolds. By themethod of bundle extensions we define a stable U(4) vector bundle leading tothe first flipped SU(5) model with just three generations, i.e. without anyvector-like matter. Along the way, we propose the notion of Lambda-stabilityfor heterotic bundles.Comment: 48 page