Comment on the Generation Number in Orbifold Compactifications

Abstract

There has been some confusion concerning the number of $(1,1)$-forms in orbifold compactifications of the heterotic string in numerous publications. In this note we point out the relevance of the underlying torus lattice on this number. We answer the question when different lattices mimic the same physics and when this is not the case. As a byproduct we classify all symmetric $Z_N$-orbifolds with $(2,2)$ world sheet supersymmetry obtaining also some new ones.

28 pages, 9 figures not included, available in postscript at request

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• Moduli Stabilization in Type IIB Orientifolds (II)
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• String GUTs
• Moduli Stabilization in Type IIB Orientifolds (I)
• Moduli Spaces and Target Space Duality Symmetries in $(0,2)Z_N$ Orbifold Theories with Continuous Wilson Lines
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• Heterotic Z6-II MSSM Orbifolds in Blowup
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• Z_2 x Z_2 Heterotic Orbifold Models of Non Factorisable Six Dimensional Toroidal Manifolds
• In quest of "just" the Standard Model on D-branes at a singularity
• Lectures on Mirror Symmetry
• Toric Resolutions of Heterotic Orbifolds
• Non-Supersymmetric Orbifolds
• Type IIA Orientifolds on General Supersymmetric Z_N Orbifolds
• $Z_N$ Orientifolds with Flux
• Non-Factorisable Z2 times Z2 Heterotic Orbifold Models and Yukawa Couplings
• Anomaly cancellation in D=4, N=1 orientifolds and linear/chiral multiplet duality
• Gauged Linear Sigma Models for toroidal orbifold resolutions
• D=4, N=1 orientifolds with vector structure
• The Geometer's Toolkit to String Compactifications
• Orientifold's Landscape: Non-Factorisable Six-Tori
• Strings on Eight-Orbifolds
• Generalized string compactifications with spontaneously broken supersymmetry
• String Loop Threshold Corrections for N=1 Generalized Coxeter Orbifolds
• Resolved Toroidal Orbifolds and their Orientifolds
• Modular Groups for Twisted Narain Models
• Moduli Stabilization in Toroidal Type IIB Orientifolds
• Orbifold Compactifications with continuous Wilson lines
• Intersecting Brane World from Type I Compactification
• Blowups of Heterotic Orbifolds using Toric Geometry
• The Master Equation for the Prepotential-Pub
• The computation of one-loop heterotic string threshold corrections for general orbifold models with discrete Wilson lines
• Massless Spectra and Gauge Couplings at One-Loop on Non-Factorisable Toroidal Orientifolds
• Toroidal Orbifolds: Resolutions, Orientifolds and Applications in String Phenomenology
• Searching singlet extensions of the supersymmetric standard model in $Z_{6-II}$ orbifold compactification of heterotic string
• Classification of (2,2) Compactifications by Free Fermions 2
• Classification of Modular Symmetries in Type IIB Flux Landscape