Massless Spectra of Three Generation U(N) Heterotic String Vacua

TL;DR

This paper develops methods to compute the complete massless spectra of certain heterotic string models with U(N) bundles on Calabi-Yau manifolds, leading to realistic three-generation flipped SU(5) models.

Contribution

It introduces a novel computational approach using Leray spectral sequences and bundle extensions to analyze heterotic string vacua with U(N) bundles, achieving models with three generations and no vector-like matter.

Findings

Derived localization of cohomology groups for vector bundles on elliptically fibered Calabi-Yau manifolds.

Constructed the first flipped SU(5) model with exactly three generations.

Proposed the concept of Lambda-stability for heterotic bundles.

Abstract

We provide the methods to compute the complete massless spectra of a class of recently introduced supersymmetric E8 x E8 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 \times V_b), H^i(X,\bigwedge^2 V) and H^i(X,{\bf 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 Lambda-stability for heterotic bundles.