Toric resolutions of heterotic orbifolds

2007/07/24 by Stefan Groot Nibbelink, Tae-Won Ha, Michele Trapletti
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Codimension #Geometry #Gravitational singularity #Heterotic string theory #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Orbifold #Physics #Pure mathematics #hep-th

paper · pdf · doi:10.1103/physrevd.77.026002

published as Phys.Rev.D77:026002,2008 · 1+34 pages LaTeX with 5 figures, some wording changed and references added

arxiv created 2007/07/24 · openalex publication_date 2008/01/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We investigate resolutions of heterotic orbifolds using toric geometry. Our starting point is provided by the recently constructed heterotic models on explicit blowup of ℂⁿ/ℤ_n singularities. We show that the values of the relevant integrals, computed there, can be obtained as integrals of divisors (complex codimension one hypersurfaces) interpreted as (1, 1)-forms in toric geometry. Motivated by this we give a self-contained introduction to toric geometry for nonexperts, focusing on those issues relevant for the construction of heterotic models on toric orbifold resolutions. We illustrate the methods by building heterotic models on the resolutions of ℂ²/ℤ₃, ℂ³/ℤ₄, and ℂ³/ℤ₂\ifmmode×\else\texttimes\fiℤ₂^\ensuremath'. We are able to obtain a direct identification between them and the known orbifold models. In the ℂ³/ℤ₂\ifmmode×\else\texttimes\fiℤ₂^\ensuremath' case we observe that, in spite of the existence of two inequivalent resolutions, fully consistent blowup models of heterotic orbifolds can only be constructed on one of them.

Citations

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