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Resolved Toroidal Orbifolds and their Orientifolds

D. Lust, S. Reffert, E. Scheidegger, S. Stieberger

Abstract

We discuss the resolution of toroidal orbifolds. For the resulting smooth Calabi-Yau manifolds, we calculate the intersection ring and determine the divisor topologies. In a next step, the orientifold quotients are constructed.

Resolved Toroidal Orbifolds and their Orientifolds

Abstract

We discuss the resolution of toroidal orbifolds. For the resulting smooth Calabi-Yau manifolds, we calculate the intersection ring and determine the divisor topologies. In a next step, the orientifold quotients are constructed.

Paper Structure

This paper contains 69 sections, 241 equations, 36 figures, 18 tables.

Table of Contents

  1. Introduction
  2. Type IIB orientifolds of toroidal orbifolds
  3. The local models
  4. Toric geometry and resolution of singularities
  5. Topology of the exceptional divisors
  6. Examples
  7. Resolution of $\mathbb{C}^3/\mathbb{Z}_{6-I}$
  8. The global models
  9. The fixed point sets and the divisors
  10. Linear relations and the intersection ring
  11. Divisor topologies
  12. Twisted complex structure moduli
  13. Examples
  14. The $\mathbb{Z}_{6-I}$ orbifold on $G_2\times SU(3)^2$
  15. The $\mathbb{Z}_{6-I}$ orbifold on $G_2^2\times SU(3)$
  16. ...and 54 more sections

Figures (36)

  • Figure 3.1: Toric diagram of $\mathbb{C}^3/\mathbb{Z}_{6-I}$ and dual graph
  • Figure 3.2: Toric diagram of the resolution of $\mathbb{C}^3/\mathbb{Z}_{6-I}$ and dual graph
  • Figure 3.3: The stars of the exceptional divisors $E_1$, $E_2$, and $E_3$, respectively.
  • Figure 4.1: The fundamental domains of $T^2/\mathbb{Z}_k$, $k=3,4,6$. The dashed line indicates the folding.
  • Figure 4.2: Schematic picture of the fixed point set of the $\mathbb{Z}_{6-I}$ orbifold on $G_2\times SU(3)^2$
  • ...and 31 more figures